124 Publications

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[124]
2021 | Journal Article | IST-REx-ID: 9412 | OA
G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.
View | Files available | DOI | arXiv
 
[123]
2021 | Journal Article | IST-REx-ID: 9550 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.
View | Files available | DOI | arXiv
 
[122]
2020 | Journal Article | IST-REx-ID: 8601 | OA
G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2020.
View | Files available | DOI | arXiv
 
[121]
2020 | Journal Article | IST-REx-ID: 7512 | OA
L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” Journal of Functional Analysis, vol. 278, no. 12. Elsevier, 2020.
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[120]
2020 | Journal Article | IST-REx-ID: 6184 | OA
J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” Annals of Probability, vol. 48, no. 2. Project Euclid, pp. 963–1001, 2020.
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[119]
2020 | Journal Article | IST-REx-ID: 6185 | OA
L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” Communications in Mathematical Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.
View | Files available | DOI | arXiv
 
[118]
2020 | Journal Article | IST-REx-ID: 6488 | OA
G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020.
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[117]
2020 | Journal Article | IST-REx-ID: 9104 | OA
Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” Journal d’Analyse Mathematique, vol. 142. Springer Nature, pp. 323–348, 2020.
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[116]
2019 | Journal Article | IST-REx-ID: 6182 | OA
L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019.
View | Files available | DOI | arXiv
 
[115]
2019 | Journal Article | IST-REx-ID: 6186 | OA
G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.
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[114]
2019 | Journal Article | IST-REx-ID: 6240 | OA
J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” Annales de l’institut Henri Poincare, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.
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[113]
2019 | Journal Article | IST-REx-ID: 6511 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.
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[112]
2019 | Journal Article | IST-REx-ID: 429 | OA
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.
View | Files available | DOI
 
[111]
2018 | Journal Article | IST-REx-ID: 181 | OA
L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018.
View | DOI | Download Published Version (ext.) | arXiv
 
[110]
2018 | Journal Article | IST-REx-ID: 566 | OA
J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics, pp. 148–203, 2018.
View | Files available | DOI | Download Preprint (ext.) | arXiv
 
[109]
2018 | Journal Article | IST-REx-ID: 5971 | OA
L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.
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[108]
2018 | Preprint | IST-REx-ID: 6183 | OA
J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and  cusps,” arXiv. .
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[107]
2018 | Journal Article | IST-REx-ID: 1012 | OA
L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.
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[106]
2017 | Journal Article | IST-REx-ID: 721 | OA
O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic vector equations on the complex upper half plane,” Communications on Pure and Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017.
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[105]
2017 | Journal Article | IST-REx-ID: 733 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” Advances in Mathematics, vol. 319. Academic Press, pp. 251–291, 2017.
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[104]
2017 | Journal Article | IST-REx-ID: 483 | OA
P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 739–800, 2017.
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[103]
2017 | Book | IST-REx-ID: 567
L. Erdös and H. Yau, A dynamical approach to random matrix theory, vol. 28. American Mathematical Society, 2017.
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[102]
2017 | Journal Article | IST-REx-ID: 615 | OA
L. Erdös and K. Schnelli, “Universality for random matrix flows with time dependent density,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656, 2017.
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[101]
2017 | Journal Article | IST-REx-ID: 1337 | OA
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type matrices,” Probability Theory and Related Fields, vol. 169, no. 3–4. Springer, pp. 667–727, 2017.
View | Files available | DOI
 
[100]
2017 | Journal Article | IST-REx-ID: 1528 | OA
Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,” Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp. 673–776, 2017.
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[99]
2017 | Journal Article | IST-REx-ID: 1010 | OA
J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017.
View | Files available | DOI | arXiv
 
[98]
2017 | Journal Article | IST-REx-ID: 1144 | OA
L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21. Institute of Mathematical Statistics, 2017.
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[97]
2017 | Journal Article | IST-REx-ID: 1207 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” Communications in Mathematical Physics, vol. 349, no. 3. Springer, pp. 947–990, 2017.
View | Files available | DOI
 
[96]
2016 | Journal Article | IST-REx-ID: 1280 | OA
P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Fixed energy universality for generalized wigner matrices,” Communications on Pure and Applied Mathematics, vol. 69, no. 10. Wiley-Blackwell, pp. 1815–1881, 2016.
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[95]
2016 | Journal Article | IST-REx-ID: 1434 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Local stability of the free additive convolution,” Journal of Functional Analysis, vol. 271, no. 3. Academic Press, pp. 672–719, 2016.
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[94]
2016 | Journal Article | IST-REx-ID: 1489 | OA
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local spectral statistics of Gaussian matrices with correlated entries,” Journal of Statistical Physics, vol. 163, no. 2. Springer, pp. 280–302, 2016.
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[93]
2015 | Journal Article | IST-REx-ID: 1864 | OA
L. Erdös and A. Knowles, “The Altshuler–Shklovskii formulas for random band matrices II: The general case,” Annales Henri Poincare, vol. 16, no. 3. Springer, pp. 709–799, 2015.
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[92]
2015 | Journal Article | IST-REx-ID: 2166 | OA
L. Erdös and A. Knowles, “The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case,” Communications in Mathematical Physics, vol. 333, no. 3. Springer, pp. 1365–1416, 2015.
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[91]
2015 | Journal Article | IST-REx-ID: 1508 | OA
L. Erdös and H. Yau, “Gap universality of generalized Wigner and β ensembles,” Journal of the European Mathematical Society, vol. 17, no. 8. European Mathematical Society, pp. 1927–2036, 2015.
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[90]
2014 | Journal Article | IST-REx-ID: 2699 | OA
L. Erdös, P. Bourgade, and H. Yau, “Universality of general β-ensembles,” Duke Mathematical Journal, vol. 163, no. 6. Duke University Press, pp. 1127–1190, 2014.
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[89]
2014 | Journal Article | IST-REx-ID: 1937 | OA
P. Bourgade, L. Erdös, and H. Yau, “Edge universality of beta ensembles,” Communications in Mathematical Physics, vol. 332, no. 1. Springer, pp. 261–353, 2014.
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[88]
2014 | Journal Article | IST-REx-ID: 2019 | OA
L. Erdös and D. J. Schröder, “Phase transition in the density of states of quantum spin glasses,” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4. Springer, pp. 441–464, 2014.
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[87]
2014 | Journal Article | IST-REx-ID: 2179 | OA
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local semicircle law with imprimitive variance matrix,” Electronic Communications in Probability, vol. 19. Institute of Mathematical Statistics, 2014.
View | Files available | DOI
 
[86]
2014 | Journal Article | IST-REx-ID: 2225 | OA
A. Bloemendal, L. Erdös, A. Knowles, H. Yau, and J. Yin, “Isotropic local laws for sample covariance and generalized Wigner matrices,” Electronic Journal of Probability, vol. 19. Institute of Mathematical Statistics, 2014.
View | Files available | DOI
 
[85]
2014 | Conference Paper | IST-REx-ID: 1507 | OA
L. Erdös, “Random matrices, log-gases and Hölder regularity,” presented at the ICM: International Congress of Mathematicians, Seoul, Korea, 2014, vol. 3, pp. 214–236.
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[84]
2013 | Journal Article | IST-REx-ID: 2697 | OA
L. Erdös, A. Knowles, H. Yau, and J. Yin, “Delocalization and diffusion profile for random band matrices,” Communications in Mathematical Physics, vol. 323, no. 1. Springer, pp. 367–416, 2013.
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[83]
2013 | Journal Article | IST-REx-ID: 2698 | OA
L. Erdös, S. Fournais, and J. Solovej, “Stability and semiclassics in self-generated fields,” Journal of the European Mathematical Society, vol. 15, no. 6. European Mathematical Society, pp. 2093–2113, 2013.
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[82]
2013 | Journal Article | IST-REx-ID: 2780 | OA
L. Erdös, A. Knowles, and H. Yau, “Averaging fluctuations in resolvents of random band matrices,” Annales Henri Poincare, vol. 14, no. 8. Birkhäuser, pp. 1837–1926, 2013.
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[81]
2013 | Journal Article | IST-REx-ID: 2781 | OA
L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erdős-Rényi graphs I: Local semicircle law,” Annals of Probability, vol. 41, no. 3 B. Institute of Mathematical Statistics, pp. 2279–2375, 2013.
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[80]
2013 | Journal Article | IST-REx-ID: 2782 | OA
L. Erdös and B. Farrell, “Local eigenvalue density for general MANOVA matrices,” Journal of Statistical Physics, vol. 152, no. 6. Springer, pp. 1003–1032, 2013.
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[79]
2013 | Journal Article | IST-REx-ID: 2837 | OA
L. Erdös, A. Knowles, H. Yau, and J. Yin, “The local semicircle law for a general class of random matrices,” Electronic Journal of Probability, vol. 18, no. 59. Institute of Mathematical Statistics, pp. 1–58, 2013.
View | Files available | DOI
 
[78]
2012 | Preprint | IST-REx-ID: 2696 | OA
L. Erdös, “Universality for random matrices and log-gases,” ArXiv. ArXiv, 2012.
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[77]
2012 | Conference Paper | IST-REx-ID: 2700 | OA
L. Erdös, “Lecture notes on quantum Brownian motion,” presented at the Les Houches Summer School 2010, 2012, vol. 95, pp. 3–98.
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[76]
2012 | Journal Article | IST-REx-ID: 2767
L. Erdös, H. Yau, and J. Yin, “Bulk universality for generalized Wigner matrices,” Probability Theory and Related Fields, vol. 154, no. 1–2. Springer, pp. 341–407, 2012.
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[75]
2012 | Journal Article | IST-REx-ID: 2768
L. Erdös and D. Hasler, “Wegner estimate and Anderson localization for random magnetic fields,” Communications in Mathematical Physics, vol. 309, no. 2. Springer, pp. 507–542, 2012.
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[74]
2012 | Journal Article | IST-REx-ID: 2769
L. Erdös, B. Schlein, H. Yau, and J. Yin, “The local relaxation flow approach to universality of the local statistics for random matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 48, no. 1. Institute of Mathematical Statistics, pp. 1–46, 2012.
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[73]
2012 | Journal Article | IST-REx-ID: 2770
L. Erdös, H. Yau, and J. Yin, “Rigidity of eigenvalues of generalized Wigner matrices,” Advances in Mathematics, vol. 229, no. 3. Academic Press, pp. 1435–1515, 2012.
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[72]
2012 | Journal Article | IST-REx-ID: 2771
L. Erdös and D. Hasler, “Anderson localization at band edges for random magnetic fields,” Journal of Statistical Physics, vol. 146, no. 5. Springer, pp. 900–923, 2012.
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[71]
2012 | Journal Article | IST-REx-ID: 2772
L. Erdös, S. Fournais, and J. Solovej, “Second order semiclassics with self generated magnetic fields,” Annales Henri Poincare, vol. 13, no. 4. Birkhäuser, pp. 671–730, 2012.
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[70]
2012 | Journal Article | IST-REx-ID: 2773
L. Erdös and H. Yau, “A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices,” Electronic Journal of Probability, vol. 17. Institute of Mathematical Statistics, 2012.
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[69]
2012 | Journal Article | IST-REx-ID: 2774
L. Erdös, S. Fournais, and J. Solovej, “Scott correction for large atoms and molecules in a self-generated magnetic field,” Communications in Mathematical Physics, vol. 312, no. 3. Springer, pp. 847–882, 2012.
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[68]
2012 | Journal Article | IST-REx-ID: 2775
L. Erdös and H. Yau, “Universality of local spectral statistics of random matrices,” Bulletin of the American Mathematical Society, vol. 49, no. 3. American Mathematical Society, pp. 377–414, 2012.
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[67]
2012 | Journal Article | IST-REx-ID: 2776
L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues,” Communications in Mathematical Physics, vol. 314, no. 3. Springer, pp. 587–640, 2012.
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[66]
2012 | Journal Article | IST-REx-ID: 2777
L. Erdös, S. Fournais, and J. Solovej, “Relativistic Scott correction in self-generated magnetic fields,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012.
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[65]
2012 | Journal Article | IST-REx-ID: 2778
P. Bourgade, L. Erdös, and H. Yau, “Bulk universality of general β-ensembles with non-convex potential,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012.
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[64]
2012 | Journal Article | IST-REx-ID: 2779
L. Erdös and D. Hasler, “Wegner estimate for random magnetic Laplacian on ℤ 2,” Annales Henri Poincare, vol. 13, no. 8. Birkhäuser, pp. 1719–1731, 2012.
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[63]
2011 | Journal Article | IST-REx-ID: 2717
L. Erdös and A. Knowles, “Quantum diffusion and eigenfunction delocalization in a random band matrix model,” Communications in Mathematical Physics, vol. 303, no. 2. Springer, pp. 509–554, 2011.
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[62]
2011 | Journal Article | IST-REx-ID: 2764
L. Erdös, B. Schlein, and H. Yau, “Universality of random matrices and local relaxation flow,” Inventiones Mathematicae, vol. 185, no. 1. Springer, pp. 75–119, 2011.
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[61]
2011 | Book Review | IST-REx-ID: 2765
L. Erdös, “Universality of Wigner random matrices: A survey of recent results,” Russian Mathematical Surveys, vol. 66, no. 3. IOP Publishing Ltd., pp. 507–626, 2011.
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[60]
2011 | Journal Article | IST-REx-ID: 2766
L. Erdös and A. Knowles, “Quantum diffusion and delocalization for band matrices with general distribution,” Annales Henri Poincare, vol. 12, no. 7. Birkhäuser, pp. 1227–1319, 2011.
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[59]
2010 | Journal Article | IST-REx-ID: 2701 | OA
L. Erdös, B. Schlein, and H. Yau, “Wegner estimate and level repulsion for Wigner random matrices,” International Mathematics Research Notices, no. 3. Oxford University Press, pp. 436–479, 2010.
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[58]
2010 | Journal Article | IST-REx-ID: 2704
L. Erdös, B. Schlein, and H. Yau, “Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate,” Annals of Mathematics, vol. 172, no. 1. Princeton University Press, pp. 291–370, 2010.
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[57]
2010 | Journal Article | IST-REx-ID: 2756
L. Erdös and J. Solovej, “Ground state energy of large atoms in a self-generated magnetic field,” Communications in Mathematical Physics, vol. 294, no. 1. Springer, pp. 229–249, 2010.
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[56]
2010 | Journal Article | IST-REx-ID: 2761
L. Erdös, J. Ramírez, B. Schlein, and H. Yau, “Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation,” Electronic Journal of Probability, vol. 15, no. 18. Institute of Mathematical Statistics, pp. 526–603, 2010.
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[55]
2010 | Journal Article | IST-REx-ID: 2762
L. Erdös, J. Ramírez, H. Yau, S. Péché, and B. Schlein, “Bulk universality for Wigner matrices,” Communications on Pure and Applied Mathematics, vol. 63, no. 7. Wiley-Blackwell, pp. 895–925, 2010.
View | DOI
 
[54]
2010 | Journal Article | IST-REx-ID: 2763
L. Erdös, J. Ramírez, B. Schlein, T. Tao, V. Van, and H. Yau, “Bulk universality for Wigner Hermitian matrices with subexponential decay,” Mathematical Research Letters, vol. 17, no. 4. International Press, pp. 667–674, 2010.
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[53]
2009 | Journal Article | IST-REx-ID: 2703
L. Erdös, B. Schlein, and H. Yau, “Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices,” Annals of Probability, vol. 37, no. 3. Institute of Mathematical Statistics, pp. 815–852, 2009.
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[52]
2009 | Journal Article | IST-REx-ID: 2757
L. Erdös and B. Schlein, “Quantum dynamics with mean field interactions: A new approach,” Journal of Statistical Physics, vol. 134, no. 5–6. Springer, pp. 859–870, 2009.
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[51]
2009 | Journal Article | IST-REx-ID: 2758
L. Erdös, B. Schlein, and H. Yau, “Local semicircle law and complete delocalization for Wigner random matrices,” Communications in Mathematical Physics, vol. 287, no. 2. Springer, pp. 641–655, 2009.
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[50]
2009 | Journal Article | IST-REx-ID: 2759
L. Erdös, A. Michelangeli, and B. Schlein, “Dynamical formation of correlations in a Bose-Einstein condensate,” Communications in Mathematical Physics, vol. 289, no. 3. Springer, pp. 1171–1210, 2009.
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[49]
2009 | Journal Article | IST-REx-ID: 2760
L. Erdös, B. Schlein, and H. Yau, “Rigorous derivation of the gross-pitaevskii equation with a large interaction potential,” Journal of the American Mathematical Society, vol. 22, no. 4. American Mathematical Society, pp. 1099–1156, 2009.
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[48]
2008 | Conference Paper | IST-REx-ID: 2702 | OA
L. Erdös, M. Salmhofer, and H. Yau, “Feynman graphs and renormalization in quantum diffusion,” presented at the Symposium in Honor of Wolfhart Zimmermann’s 80th Birthday, 2008, pp. 167–182.
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[47]
2008 | Journal Article | IST-REx-ID: 2753
L. Erdös, M. Salmhofer, and H. Yau, “Quantum diffusion of the random Schrödinger evolution in the scaling limit,” Acta Mathematica, vol. 200, no. 2. Springer, pp. 211–277, 2008.
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[46]
2008 | Journal Article | IST-REx-ID: 2754
R. Adami and L. Erdös, “Rate of decoherence for an electron weakly coupled to a phonon gas,” Journal of Statistical Physics, vol. 132, no. 2. Springer, pp. 301–328, 2008.
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[45]
2008 | Journal Article | IST-REx-ID: 2755
L. Erdös, B. Schlein, and H. Yau, “Ground-state energy of a low-density Bose gas: A second-order upper bound,” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 78, no. 5. American Physical Society, 2008.
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[44]
2007 | Book Chapter | IST-REx-ID: 2705 | OA
L. Erdös, “Recent developments in quantum mechanics with magnetic fields,” in Spectral Theory and Mathematical Physics: a Festschrift in Honor of Barry Simon’s 60th Birthday , vol. 76, F. Gesztesy, P. Deift, P. Galvez, P. Perry, and W. Schlag, Eds. American Mathematical Society, 2007, pp. 401–428.
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[43]
2007 | Journal Article | IST-REx-ID: 2748
L. Erdös, B. Schlein, and H. Yau, “Rigorous derivation of the Gross-Pitaevskii equation,” Physical Review Letters, vol. 98, no. 4. American Physical Society, 2007.
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[42]
2007 | Book Review | IST-REx-ID: 2749
L. Erdös, B. Schlein, and H. Yau, “Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems,” Inventiones Mathematicae, vol. 167, no. 3. Springer, pp. 515–614, 2007.
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[41]
2007 | Journal Article | IST-REx-ID: 2750
L. Erdös, M. Salmhofer, and H. Yau, “Quantum diffusion of the random Schrödinger evolution in the scaling limit II. The recollision diagrams,” Communications in Mathematical Physics, vol. 271, no. 1. Springer, pp. 1–53, 2007.
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[40]
2007 | Journal Article | IST-REx-ID: 2751
L. Erdös, M. Salmhofer, and H. Yau, “Quantum diffusion for the Anderson model in the scaling limit,” Annales Henri Poincare, vol. 8, no. 4. Birkhäuser, pp. 621–685, 2007.
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[39]
2007 | Journal Article | IST-REx-ID: 2752
L. Erdös and M. Salmhofer, “Decay of the Fourier transform of surfaces with vanishing curvature,” Mathematische Zeitschrift, vol. 257, no. 2. Springer, pp. 261–294, 2007.
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[38]
2006 | Journal Article | IST-REx-ID: 2745
A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons,” Archive for Rational Mechanics and Analysis, vol. 179, no. 2. Springer, pp. 265–283, 2006.
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[37]
2006 | Conference Paper | IST-REx-ID: 2746
L. Erdös, M. Salmhofer, and H. Yau, “Towards the quantum Brownian motion,” presented at the QMath: Mathematical Results in Quantum Physics, 2006, vol. 690, pp. 233–257.
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[36]
2006 | Journal Article | IST-REx-ID: 2747
L. Erdös, B. Schlein, and H. Yau, “Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate,” Communications on Pure and Applied Mathematics, vol. 59, no. 12. Wiley-Blackwell, pp. 1659–1741, 2006.
View | DOI
 
[35]
2005 | Journal Article | IST-REx-ID: 2743
L. Erdös, D. Hasler, and J. Solovej, “Existence of the D0-D4 bound state: A detailed proof,” Annales Henri Poincare, vol. 6, no. 2. Birkhäuser, pp. 247–267, 2005.
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[34]
2005 | Journal Article | IST-REx-ID: 2744
D. Eng and L. Erdös, “The linear Boltzmann equation as the low density limit of a random Schrödinger equation,” Reviews in Mathematical Physics, vol. 17, no. 6. World Scientific Publishing, pp. 669–743, 2005.
View | DOI
 
[33]
2004 | Journal Article | IST-REx-ID: 2706
L. Erdös and J. Solovej, “Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength,” Journal of Statistical Physics, vol. 116, no. 1–4. Springer, pp. 475–506, 2004.
View | DOI
 
[32]
2004 | Journal Article | IST-REx-ID: 2707
L. Erdös, M. Salmhofer, and H. Yau, “On the quantum Boltzmann equation,” Journal of Statistical Physics, vol. 116, no. 1–4. Springer, pp. 367–380, 2004.
View | DOI
 
[31]
2004 | Journal Article | IST-REx-ID: 2741
L. Erdös and J. Solovej, “Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field,” Annales Henri Poincare, vol. 5, no. 4. Birkhäuser, pp. 671–741, 2004.
View | DOI
 
[30]
2004 | Journal Article | IST-REx-ID: 2742
A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Nonlinear Hartree equation as the mean field limit of weakly coupled fermions,” Journal de Mathématiques Pures et Appliquées, vol. 83, no. 10. Elsevier, pp. 1241–1273, 2004.
View | DOI
 
[29]
2002 | Conference Paper | IST-REx-ID: 2694
L. Erdös, “Scaling limits of Schrödinger quantum mechanics,” presented at the 38th Winter School of Theoretical Physics : Dynamical Semigroups: Dissipation, Chaos, Quanta, 2002, vol. 597, pp. 487–506.
View | DOI
 
[28]
2002 | Conference Paper | IST-REx-ID: 2708
L. Erdös, “Two dimensional Pauli operator via scalar potential,” presented at the QMath: Mathematical Results in Quantum Physics, 2002, vol. 307, pp. 129–133.
View | DOI
 
[27]
2002 | Journal Article | IST-REx-ID: 2737
C. Bardos, L. Erdös, F. Golse, N. Mauser, and H. Yau, “Derivation of the Schrödinger-Poisson equation from the quantum N-body problem,” Comptes Rendus Mathematique, vol. 334, no. 6. Elsevier, pp. 515–520, 2002.
View | DOI
 
[26]
2002 | Journal Article | IST-REx-ID: 2738
L. Erdös, “Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field,” Journal of Statistical Physics, vol. 107, no. 5–6. Springer, pp. 1043–1127, 2002.
View | DOI
 
[25]
2002 | Journal Article | IST-REx-ID: 2739
L. Erdös and V. Vougalter, “Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields,” Communications in Mathematical Physics, vol. 225, no. 2. Springer, pp. 399–421, 2002.
View | DOI
 
[24]
2002 | Journal Article | IST-REx-ID: 2740
L. Erdös, “Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions,” Annales de l’Institut Fourier, vol. 52, no. 6. Association des Annales de l’Institut Fourier, p. 1833–1874+XI+VII, 2002.
View | DOI
 
[23]
2001 | Journal Article | IST-REx-ID: 2709
L. Erdös, “Long time dynamics of an electron in a weakly coupled phonon field,” ICMP: International Congress on Mathematical Physics. World Scientific Publishing, pp. 273–281, 2001.
View
 
[22]
2001 | Journal Article | IST-REx-ID: 2734
L. Erdös and J. Solovej, “The kernel of Dirac operators on S3 and R3,” Reviews in Mathematical Physics, vol. 13, no. 10. World Scientific Publishing, pp. 1247–1280, 2001.
View | DOI
 
[21]
2001 | Journal Article | IST-REx-ID: 2735
L. Erdös, “Lifschitz tail in a magnetic field: Coexistence of classical and quantum behavior in the borderline case,” Probability Theory and Related Fields, vol. 121, no. 2. Springer, pp. 219–236, 2001.
View | DOI
 
[20]
2001 | Journal Article | IST-REx-ID: 2736 | OA
L. Erdös and H. Yau, “Derivation of the nonlinear Schrödinger equation from a many body Coulomb system,” Advances in Theoretical and Mathematical Physics, vol. 5, no. 6. International Press, pp. 1169–1205, 2001.
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[19]
2000 | Conference Paper | IST-REx-ID: 2710
L. Erdös, “The kernel of Dirac operators on S3 and R3,” presented at the Differential Equations and Mathematical Physics, 2000, vol. 16, pp. 111–119.
View
 
[18]
2000 | Journal Article | IST-REx-ID: 2731
L. Erdös and H. Yau, “Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation,” Communications on Pure and Applied Mathematics, vol. 53, no. 6. Wiley-Blackwell, pp. 667–735, 2000.
View | DOI
 
[17]
2000 | Journal Article | IST-REx-ID: 2732
F. Castella, L. Erdös, F. Frommlet, and P. Markowich, “Fokker-Planck equations as scaling limits of reversible quantum systems,” Journal of Statistical Physics, vol. 100, no. 3–4. Springer, pp. 543–601, 2000.
View | DOI
 
[16]
2000 | Journal Article | IST-REx-ID: 2733
L. Erdös, M. Loss, and V. Vougalter, “Diamagnetic behavior of sums Dirichlet eigenvalues,” Annales de l’Institut Fourier, vol. 50, no. 3. Association des Annales de l’Institut Fourier, pp. 891–907, 2000.
View | DOI
 
[15]
1999 | Conference Paper | IST-REx-ID: 2711
L. Erdös, “Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation,” presented at the QMath: Mathematical Results in Quantum Physics, 1999, vol. 108, pp. 233–242.
View | DOI
 
[14]
1999 | Journal Article | IST-REx-ID: 2730
L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate,” Duke Mathematical Journal, vol. 96, no. 1. Duke University Press, pp. 127–173, 1999.
View | DOI
 
[13]
1998 | Conference Paper | IST-REx-ID: 2695
L. Erdös and H. Yau, “Linear Boltzmann equation as scaling limit of quantum Lorentz gas,” presented at the Differential Equations and Mathematical Physics, 1998, vol. 217, pp. 137–155.
View | DOI
 
[12]
1998 | Journal Article | IST-REx-ID: 2728
L. Erdös, “Lifschitz tail in a magnetic field: The nonclassical regime,” Probability Theory and Related Fields, vol. 112, no. 3. Springer, pp. 321–371, 1998.
View | DOI
 
[11]
1997 | Journal Article | IST-REx-ID: 2727
L. Erdös, “Dia- and paramagnetism for nonhomogeneous magnetic fields,” Journal of Mathematical Physics, vol. 38, no. 3. American Institute of Physics, pp. 1289–1317, 1997.
View | DOI
 
[10]
1997 | Journal Article | IST-REx-ID: 2729
L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates,” Communications in Mathematical Physics, vol. 188, no. 3. Springer, pp. 599–656, 1997.
View | DOI
 
[9]
1996 | Journal Article | IST-REx-ID: 2725
L. Erdös, “Rayleigh-type isoperimetric inequality with a homogeneous magnetic field,” Calculus of Variations and Partial Differential Equations, vol. 4, no. 3. Springer, pp. 283–292, 1996.
View | DOI
 
[8]
1996 | Journal Article | IST-REx-ID: 2726
L. Erdös, “Gaussian decay of the magnetic eigenfunctions,” Geometric and Functional Analysis, vol. 6, no. 2. Birkhäuser, pp. 231–248, 1996.
View | DOI
 
[7]
1995 | Conference Paper | IST-REx-ID: 2712
L. Erdös, “Magnetic Lieb-Thirring inequalities and stochastic oscillatory integrals,” presented at the Partial Differential Operators and Mathematical Physics, 1995, vol. 78, pp. 127–132.
View | DOI
 
[6]
1995 | Journal Article | IST-REx-ID: 2724
L. Erdös, “Magnetic Lieb-Thirring inequalities,” Communications in Mathematical Physics, vol. 170, no. 3. Springer, pp. 629–668, 1995.
View | DOI
 
[5]
1994 | Journal Article | IST-REx-ID: 2713
L. Erdös, “Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator,” Duke Mathematical Journal, vol. 76, no. 2. Duke University Press, pp. 541–566, 1994.
View | DOI
 
[4]
1993 | Journal Article | IST-REx-ID: 2723
L. Erdös, “Ground-state density of the Pauli operator in the large field limit,” Letters in Mathematical Physics, vol. 29, no. 3. Springer, pp. 219–240, 1993.
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[3]
1992 | Journal Article | IST-REx-ID: 2714
L. Erdös, “On some problems of P. Turán concerning power sums of complex numbers,” Acta Mathematica Hungarica, vol. 59, no. 1–2. Springer, pp. 11–24, 1992.
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[2]
1992 | Journal Article | IST-REx-ID: 2722
L. Erdös and D. Tuyen, “Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers,” Communications in Mathematical Physics, vol. 143, no. 3. Springer, pp. 451–466, 1992.
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[1]
1990 | Journal Article | IST-REx-ID: 2721
L. Erdös and D. Tuyen, “Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier,” Journal of Statistical Physics, vol. 59, no. 5–6. Springer, pp. 1589–1602, 1990.
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[124]
2021 | Journal Article | IST-REx-ID: 9412 | OA
G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.
View | Files available | DOI | arXiv
 
[123]
2021 | Journal Article | IST-REx-ID: 9550 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.
View | Files available | DOI | arXiv
 
[122]
2020 | Journal Article | IST-REx-ID: 8601 | OA
G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2020.
View | Files available | DOI | arXiv
 
[121]
2020 | Journal Article | IST-REx-ID: 7512 | OA
L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” Journal of Functional Analysis, vol. 278, no. 12. Elsevier, 2020.
View | DOI | Download Preprint (ext.) | arXiv
 
[120]
2020 | Journal Article | IST-REx-ID: 6184 | OA
J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” Annals of Probability, vol. 48, no. 2. Project Euclid, pp. 963–1001, 2020.
View | Files available | Download Preprint (ext.) | arXiv
 
[119]
2020 | Journal Article | IST-REx-ID: 6185 | OA
L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” Communications in Mathematical Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.
View | Files available | DOI | arXiv
 
[118]
2020 | Journal Article | IST-REx-ID: 6488 | OA
G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020.
View | DOI | Download Preprint (ext.) | arXiv
 
[117]
2020 | Journal Article | IST-REx-ID: 9104 | OA
Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” Journal d’Analyse Mathematique, vol. 142. Springer Nature, pp. 323–348, 2020.
View | DOI | Download Preprint (ext.) | arXiv
 
[116]
2019 | Journal Article | IST-REx-ID: 6182 | OA
L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019.
View | Files available | DOI | arXiv
 
[115]
2019 | Journal Article | IST-REx-ID: 6186 | OA
G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.
View | Files available | DOI | Download Preprint (ext.) | arXiv
 
[114]
2019 | Journal Article | IST-REx-ID: 6240 | OA
J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” Annales de l’institut Henri Poincare, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.
View | Files available | DOI | Download Preprint (ext.) | arXiv
 
[113]
2019 | Journal Article | IST-REx-ID: 6511 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.
View | DOI | Download Preprint (ext.) | arXiv
 
[112]
2019 | Journal Article | IST-REx-ID: 429 | OA
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.
View | Files available | DOI
 
[111]
2018 | Journal Article | IST-REx-ID: 181 | OA
L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018.
View | DOI | Download Published Version (ext.) | arXiv
 
[110]
2018 | Journal Article | IST-REx-ID: 566 | OA
J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics, pp. 148–203, 2018.
View | Files available | DOI | Download Preprint (ext.) | arXiv
 
[109]
2018 | Journal Article | IST-REx-ID: 5971 | OA
L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.
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[108]
2018 | Preprint | IST-REx-ID: 6183 | OA
J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and  cusps,” arXiv. .
View | Files available | Download Preprint (ext.) | arXiv
 
[107]
2018 | Journal Article | IST-REx-ID: 1012 | OA
L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.
View | Files available | DOI | Download Preprint (ext.) | arXiv
 
[106]
2017 | Journal Article | IST-REx-ID: 721 | OA
O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic vector equations on the complex upper half plane,” Communications on Pure and Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017.
View | DOI | Download Submitted Version (ext.)
 
[105]
2017 | Journal Article | IST-REx-ID: 733 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” Advances in Mathematics, vol. 319. Academic Press, pp. 251–291, 2017.
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[104]
2017 | Journal Article | IST-REx-ID: 483 | OA
P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 739–800, 2017.
View | DOI | Download Submitted Version (ext.)
 
[103]
2017 | Book | IST-REx-ID: 567
L. Erdös and H. Yau, A dynamical approach to random matrix theory, vol. 28. American Mathematical Society, 2017.
View
 
[102]
2017 | Journal Article | IST-REx-ID: 615 | OA
L. Erdös and K. Schnelli, “Universality for random matrix flows with time dependent density,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656, 2017.
View | DOI | Download Submitted Version (ext.)
 
[101]
2017 | Journal Article | IST-REx-ID: 1337 | OA
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type matrices,” Probability Theory and Related Fields, vol. 169, no. 3–4. Springer, pp. 667–727, 2017.
View | Files available | DOI
 
[100]
2017 | Journal Article | IST-REx-ID: 1528 | OA
Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,” Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp. 673–776, 2017.
View | Files available | DOI
 
[99]
2017 | Journal Article | IST-REx-ID: 1010 | OA
J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017.
View | Files available | DOI | arXiv
 
[98]
2017 | Journal Article | IST-REx-ID: 1144 | OA
L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21. Institute of Mathematical Statistics, 2017.
View | Files available | DOI
 
[97]
2017 | Journal Article | IST-REx-ID: 1207 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” Communications in Mathematical Physics, vol. 349, no. 3. Springer, pp. 947–990, 2017.
View | Files available | DOI
 
[96]
2016 | Journal Article | IST-REx-ID: 1280 | OA
P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Fixed energy universality for generalized wigner matrices,” Communications on Pure and Applied Mathematics, vol. 69, no. 10. Wiley-Blackwell, pp. 1815–1881, 2016.
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[95]
2016 | Journal Article | IST-REx-ID: 1434 | OA
Z. Bao, L. Erdös, and K. Schnelli, “Local stability of the free additive convolution,” Journal of Functional Analysis, vol. 271, no. 3. Academic Press, pp. 672–719, 2016.
View | DOI | Download Preprint (ext.)
 
[94]
2016 | Journal Article | IST-REx-ID: 1489 | OA
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local spectral statistics of Gaussian matrices with correlated entries,” Journal of Statistical Physics, vol. 163, no. 2. Springer, pp. 280–302, 2016.
View | Files available | DOI
 
[93]
2015 | Journal Article | IST-REx-ID: 1864 | OA
L. Erdös and A. Knowles, “The Altshuler–Shklovskii formulas for random band matrices II: The general case,” Annales Henri Poincare, vol. 16, no. 3. Springer, pp. 709–799, 2015.
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[92]
2015 | Journal Article | IST-REx-ID: 2166 | OA
L. Erdös and A. Knowles, “The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case,” Communications in Mathematical Physics, vol. 333, no. 3. Springer, pp. 1365–1416, 2015.
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[91]
2015 | Journal Article | IST-REx-ID: 1508 | OA
L. Erdös and H. Yau, “Gap universality of generalized Wigner and β ensembles,” Journal of the European Mathematical Society, vol. 17, no. 8. European Mathematical Society, pp. 1927–2036, 2015.
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[90]
2014 | Journal Article | IST-REx-ID: 2699 | OA
L. Erdös, P. Bourgade, and H. Yau, “Universality of general β-ensembles,” Duke Mathematical Journal, vol. 163, no. 6. Duke University Press, pp. 1127–1190, 2014.
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[89]
2014 | Journal Article | IST-REx-ID: 1937 | OA
P. Bourgade, L. Erdös, and H. Yau, “Edge universality of beta ensembles,” Communications in Mathematical Physics, vol. 332, no. 1. Springer, pp. 261–353, 2014.
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[88]
2014 | Journal Article | IST-REx-ID: 2019 | OA
L. Erdös and D. J. Schröder, “Phase transition in the density of states of quantum spin glasses,” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4. Springer, pp. 441–464, 2014.
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[87]
2014 | Journal Article | IST-REx-ID: 2179 | OA
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local semicircle law with imprimitive variance matrix,” Electronic Communications in Probability, vol. 19. Institute of Mathematical Statistics, 2014.
View | Files available | DOI
 
[86]
2014 | Journal Article | IST-REx-ID: 2225 | OA
A. Bloemendal, L. Erdös, A. Knowles, H. Yau, and J. Yin, “Isotropic local laws for sample covariance and generalized Wigner matrices,” Electronic Journal of Probability, vol. 19. Institute of Mathematical Statistics, 2014.
View | Files available | DOI
 
[85]
2014 | Conference Paper | IST-REx-ID: 1507 | OA
L. Erdös, “Random matrices, log-gases and Hölder regularity,” presented at the ICM: International Congress of Mathematicians, Seoul, Korea, 2014, vol. 3, pp. 214–236.
View | Download Submitted Version (ext.)
 
[84]
2013 | Journal Article | IST-REx-ID: 2697 | OA
L. Erdös, A. Knowles, H. Yau, and J. Yin, “Delocalization and diffusion profile for random band matrices,” Communications in Mathematical Physics, vol. 323, no. 1. Springer, pp. 367–416, 2013.
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[83]
2013 | Journal Article | IST-REx-ID: 2698 | OA
L. Erdös, S. Fournais, and J. Solovej, “Stability and semiclassics in self-generated fields,” Journal of the European Mathematical Society, vol. 15, no. 6. European Mathematical Society, pp. 2093–2113, 2013.
View | DOI | Download Preprint (ext.) | arXiv
 
[82]
2013 | Journal Article | IST-REx-ID: 2780 | OA
L. Erdös, A. Knowles, and H. Yau, “Averaging fluctuations in resolvents of random band matrices,” Annales Henri Poincare, vol. 14, no. 8. Birkhäuser, pp. 1837–1926, 2013.
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[81]
2013 | Journal Article | IST-REx-ID: 2781 | OA
L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erdős-Rényi graphs I: Local semicircle law,” Annals of Probability, vol. 41, no. 3 B. Institute of Mathematical Statistics, pp. 2279–2375, 2013.
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[80]
2013 | Journal Article | IST-REx-ID: 2782 | OA
L. Erdös and B. Farrell, “Local eigenvalue density for general MANOVA matrices,” Journal of Statistical Physics, vol. 152, no. 6. Springer, pp. 1003–1032, 2013.
View | DOI | Download Preprint (ext.) | arXiv
 
[79]
2013 | Journal Article | IST-REx-ID: 2837 | OA
L. Erdös, A. Knowles, H. Yau, and J. Yin, “The local semicircle law for a general class of random matrices,” Electronic Journal of Probability, vol. 18, no. 59. Institute of Mathematical Statistics, pp. 1–58, 2013.
View | Files available | DOI
 
[78]
2012 | Preprint | IST-REx-ID: 2696 | OA
L. Erdös, “Universality for random matrices and log-gases,” ArXiv. ArXiv, 2012.
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[77]
2012 | Conference Paper | IST-REx-ID: 2700 | OA
L. Erdös, “Lecture notes on quantum Brownian motion,” presented at the Les Houches Summer School 2010, 2012, vol. 95, pp. 3–98.
View | Download (ext.)
 
[76]
2012 | Journal Article | IST-REx-ID: 2767
L. Erdös, H. Yau, and J. Yin, “Bulk universality for generalized Wigner matrices,” Probability Theory and Related Fields, vol. 154, no. 1–2. Springer, pp. 341–407, 2012.
View | DOI
 
[75]
2012 | Journal Article | IST-REx-ID: 2768
L. Erdös and D. Hasler, “Wegner estimate and Anderson localization for random magnetic fields,” Communications in Mathematical Physics, vol. 309, no. 2. Springer, pp. 507–542, 2012.
View | DOI
 
[74]
2012 | Journal Article | IST-REx-ID: 2769
L. Erdös, B. Schlein, H. Yau, and J. Yin, “The local relaxation flow approach to universality of the local statistics for random matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 48, no. 1. Institute of Mathematical Statistics, pp. 1–46, 2012.
View | DOI
 
[73]
2012 | Journal Article | IST-REx-ID: 2770
L. Erdös, H. Yau, and J. Yin, “Rigidity of eigenvalues of generalized Wigner matrices,” Advances in Mathematics, vol. 229, no. 3. Academic Press, pp. 1435–1515, 2012.
View | DOI
 
[72]
2012 | Journal Article | IST-REx-ID: 2771
L. Erdös and D. Hasler, “Anderson localization at band edges for random magnetic fields,” Journal of Statistical Physics, vol. 146, no. 5. Springer, pp. 900–923, 2012.
View | DOI
 
[71]
2012 | Journal Article | IST-REx-ID: 2772
L. Erdös, S. Fournais, and J. Solovej, “Second order semiclassics with self generated magnetic fields,” Annales Henri Poincare, vol. 13, no. 4. Birkhäuser, pp. 671–730, 2012.
View | DOI
 
[70]
2012 | Journal Article | IST-REx-ID: 2773
L. Erdös and H. Yau, “A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices,” Electronic Journal of Probability, vol. 17. Institute of Mathematical Statistics, 2012.
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[69]
2012 | Journal Article | IST-REx-ID: 2774
L. Erdös, S. Fournais, and J. Solovej, “Scott correction for large atoms and molecules in a self-generated magnetic field,” Communications in Mathematical Physics, vol. 312, no. 3. Springer, pp. 847–882, 2012.
View | DOI
 
[68]
2012 | Journal Article | IST-REx-ID: 2775
L. Erdös and H. Yau, “Universality of local spectral statistics of random matrices,” Bulletin of the American Mathematical Society, vol. 49, no. 3. American Mathematical Society, pp. 377–414, 2012.
View | DOI
 
[67]
2012 | Journal Article | IST-REx-ID: 2776
L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues,” Communications in Mathematical Physics, vol. 314, no. 3. Springer, pp. 587–640, 2012.
View | DOI
 
[66]
2012 | Journal Article | IST-REx-ID: 2777
L. Erdös, S. Fournais, and J. Solovej, “Relativistic Scott correction in self-generated magnetic fields,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012.
View | DOI
 
[65]
2012 | Journal Article | IST-REx-ID: 2778
P. Bourgade, L. Erdös, and H. Yau, “Bulk universality of general β-ensembles with non-convex potential,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012.
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[64]
2012 | Journal Article | IST-REx-ID: 2779
L. Erdös and D. Hasler, “Wegner estimate for random magnetic Laplacian on ℤ 2,” Annales Henri Poincare, vol. 13, no. 8. Birkhäuser, pp. 1719–1731, 2012.
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[63]
2011 | Journal Article | IST-REx-ID: 2717
L. Erdös and A. Knowles, “Quantum diffusion and eigenfunction delocalization in a random band matrix model,” Communications in Mathematical Physics, vol. 303, no. 2. Springer, pp. 509–554, 2011.
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[62]
2011 | Journal Article | IST-REx-ID: 2764
L. Erdös, B. Schlein, and H. Yau, “Universality of random matrices and local relaxation flow,” Inventiones Mathematicae, vol. 185, no. 1. Springer, pp. 75–119, 2011.
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[61]
2011 | Book Review | IST-REx-ID: 2765
L. Erdös, “Universality of Wigner random matrices: A survey of recent results,” Russian Mathematical Surveys, vol. 66, no. 3. IOP Publishing Ltd., pp. 507–626, 2011.
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[60]
2011 | Journal Article | IST-REx-ID: 2766
L. Erdös and A. Knowles, “Quantum diffusion and delocalization for band matrices with general distribution,” Annales Henri Poincare, vol. 12, no. 7. Birkhäuser, pp. 1227–1319, 2011.
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[59]
2010 | Journal Article | IST-REx-ID: 2701 | OA
L. Erdös, B. Schlein, and H. Yau, “Wegner estimate and level repulsion for Wigner random matrices,” International Mathematics Research Notices, no. 3. Oxford University Press, pp. 436–479, 2010.
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[58]
2010 | Journal Article | IST-REx-ID: 2704
L. Erdös, B. Schlein, and H. Yau, “Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate,” Annals of Mathematics, vol. 172, no. 1. Princeton University Press, pp. 291–370, 2010.
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[57]
2010 | Journal Article | IST-REx-ID: 2756
L. Erdös and J. Solovej, “Ground state energy of large atoms in a self-generated magnetic field,” Communications in Mathematical Physics, vol. 294, no. 1. Springer, pp. 229–249, 2010.
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[56]
2010 | Journal Article | IST-REx-ID: 2761
L. Erdös, J. Ramírez, B. Schlein, and H. Yau, “Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation,” Electronic Journal of Probability, vol. 15, no. 18. Institute of Mathematical Statistics, pp. 526–603, 2010.
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[55]
2010 | Journal Article | IST-REx-ID: 2762
L. Erdös, J. Ramírez, H. Yau, S. Péché, and B. Schlein, “Bulk universality for Wigner matrices,” Communications on Pure and Applied Mathematics, vol. 63, no. 7. Wiley-Blackwell, pp. 895–925, 2010.
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[54]
2010 | Journal Article | IST-REx-ID: 2763
L. Erdös, J. Ramírez, B. Schlein, T. Tao, V. Van, and H. Yau, “Bulk universality for Wigner Hermitian matrices with subexponential decay,” Mathematical Research Letters, vol. 17, no. 4. International Press, pp. 667–674, 2010.
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[53]
2009 | Journal Article | IST-REx-ID: 2703
L. Erdös, B. Schlein, and H. Yau, “Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices,” Annals of Probability, vol. 37, no. 3. Institute of Mathematical Statistics, pp. 815–852, 2009.
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[52]
2009 | Journal Article | IST-REx-ID: 2757
L. Erdös and B. Schlein, “Quantum dynamics with mean field interactions: A new approach,” Journal of Statistical Physics, vol. 134, no. 5–6. Springer, pp. 859–870, 2009.
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[51]
2009 | Journal Article | IST-REx-ID: 2758
L. Erdös, B. Schlein, and H. Yau, “Local semicircle law and complete delocalization for Wigner random matrices,” Communications in Mathematical Physics, vol. 287, no. 2. Springer, pp. 641–655, 2009.
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[50]
2009 | Journal Article | IST-REx-ID: 2759
L. Erdös, A. Michelangeli, and B. Schlein, “Dynamical formation of correlations in a Bose-Einstein condensate,” Communications in Mathematical Physics, vol. 289, no. 3. Springer, pp. 1171–1210, 2009.
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[49]
2009 | Journal Article | IST-REx-ID: 2760
L. Erdös, B. Schlein, and H. Yau, “Rigorous derivation of the gross-pitaevskii equation with a large interaction potential,” Journal of the American Mathematical Society, vol. 22, no. 4. American Mathematical Society, pp. 1099–1156, 2009.
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[48]
2008 | Conference Paper | IST-REx-ID: 2702 | OA
L. Erdös, M. Salmhofer, and H. Yau, “Feynman graphs and renormalization in quantum diffusion,” presented at the Symposium in Honor of Wolfhart Zimmermann’s 80th Birthday, 2008, pp. 167–182.
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[47]
2008 | Journal Article | IST-REx-ID: 2753
L. Erdös, M. Salmhofer, and H. Yau, “Quantum diffusion of the random Schrödinger evolution in the scaling limit,” Acta Mathematica, vol. 200, no. 2. Springer, pp. 211–277, 2008.
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[46]
2008 | Journal Article | IST-REx-ID: 2754
R. Adami and L. Erdös, “Rate of decoherence for an electron weakly coupled to a phonon gas,” Journal of Statistical Physics, vol. 132, no. 2. Springer, pp. 301–328, 2008.
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[45]
2008 | Journal Article | IST-REx-ID: 2755
L. Erdös, B. Schlein, and H. Yau, “Ground-state energy of a low-density Bose gas: A second-order upper bound,” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 78, no. 5. American Physical Society, 2008.
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[44]
2007 | Book Chapter | IST-REx-ID: 2705 | OA
L. Erdös, “Recent developments in quantum mechanics with magnetic fields,” in Spectral Theory and Mathematical Physics: a Festschrift in Honor of Barry Simon’s 60th Birthday , vol. 76, F. Gesztesy, P. Deift, P. Galvez, P. Perry, and W. Schlag, Eds. American Mathematical Society, 2007, pp. 401–428.
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[43]
2007 | Journal Article | IST-REx-ID: 2748
L. Erdös, B. Schlein, and H. Yau, “Rigorous derivation of the Gross-Pitaevskii equation,” Physical Review Letters, vol. 98, no. 4. American Physical Society, 2007.
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[42]
2007 | Book Review | IST-REx-ID: 2749
L. Erdös, B. Schlein, and H. Yau, “Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems,” Inventiones Mathematicae, vol. 167, no. 3. Springer, pp. 515–614, 2007.
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[41]
2007 | Journal Article | IST-REx-ID: 2750
L. Erdös, M. Salmhofer, and H. Yau, “Quantum diffusion of the random Schrödinger evolution in the scaling limit II. The recollision diagrams,” Communications in Mathematical Physics, vol. 271, no. 1. Springer, pp. 1–53, 2007.
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[40]
2007 | Journal Article | IST-REx-ID: 2751
L. Erdös, M. Salmhofer, and H. Yau, “Quantum diffusion for the Anderson model in the scaling limit,” Annales Henri Poincare, vol. 8, no. 4. Birkhäuser, pp. 621–685, 2007.
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[39]
2007 | Journal Article | IST-REx-ID: 2752
L. Erdös and M. Salmhofer, “Decay of the Fourier transform of surfaces with vanishing curvature,” Mathematische Zeitschrift, vol. 257, no. 2. Springer, pp. 261–294, 2007.
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[38]
2006 | Journal Article | IST-REx-ID: 2745
A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons,” Archive for Rational Mechanics and Analysis, vol. 179, no. 2. Springer, pp. 265–283, 2006.
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[37]
2006 | Conference Paper | IST-REx-ID: 2746
L. Erdös, M. Salmhofer, and H. Yau, “Towards the quantum Brownian motion,” presented at the QMath: Mathematical Results in Quantum Physics, 2006, vol. 690, pp. 233–257.
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[36]
2006 | Journal Article | IST-REx-ID: 2747
L. Erdös, B. Schlein, and H. Yau, “Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate,” Communications on Pure and Applied Mathematics, vol. 59, no. 12. Wiley-Blackwell, pp. 1659–1741, 2006.
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[35]
2005 | Journal Article | IST-REx-ID: 2743
L. Erdös, D. Hasler, and J. Solovej, “Existence of the D0-D4 bound state: A detailed proof,” Annales Henri Poincare, vol. 6, no. 2. Birkhäuser, pp. 247–267, 2005.
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[34]
2005 | Journal Article | IST-REx-ID: 2744
D. Eng and L. Erdös, “The linear Boltzmann equation as the low density limit of a random Schrödinger equation,” Reviews in Mathematical Physics, vol. 17, no. 6. World Scientific Publishing, pp. 669–743, 2005.
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[33]
2004 | Journal Article | IST-REx-ID: 2706
L. Erdös and J. Solovej, “Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength,” Journal of Statistical Physics, vol. 116, no. 1–4. Springer, pp. 475–506, 2004.
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[32]
2004 | Journal Article | IST-REx-ID: 2707
L. Erdös, M. Salmhofer, and H. Yau, “On the quantum Boltzmann equation,” Journal of Statistical Physics, vol. 116, no. 1–4. Springer, pp. 367–380, 2004.
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[31]
2004 | Journal Article | IST-REx-ID: 2741
L. Erdös and J. Solovej, “Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field,” Annales Henri Poincare, vol. 5, no. 4. Birkhäuser, pp. 671–741, 2004.
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[30]
2004 | Journal Article | IST-REx-ID: 2742
A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Nonlinear Hartree equation as the mean field limit of weakly coupled fermions,” Journal de Mathématiques Pures et Appliquées, vol. 83, no. 10. Elsevier, pp. 1241–1273, 2004.
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[29]
2002 | Conference Paper | IST-REx-ID: 2694
L. Erdös, “Scaling limits of Schrödinger quantum mechanics,” presented at the 38th Winter School of Theoretical Physics : Dynamical Semigroups: Dissipation, Chaos, Quanta, 2002, vol. 597, pp. 487–506.
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[28]
2002 | Conference Paper | IST-REx-ID: 2708
L. Erdös, “Two dimensional Pauli operator via scalar potential,” presented at the QMath: Mathematical Results in Quantum Physics, 2002, vol. 307, pp. 129–133.
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[27]
2002 | Journal Article | IST-REx-ID: 2737
C. Bardos, L. Erdös, F. Golse, N. Mauser, and H. Yau, “Derivation of the Schrödinger-Poisson equation from the quantum N-body problem,” Comptes Rendus Mathematique, vol. 334, no. 6. Elsevier, pp. 515–520, 2002.
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[26]
2002 | Journal Article | IST-REx-ID: 2738
L. Erdös, “Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field,” Journal of Statistical Physics, vol. 107, no. 5–6. Springer, pp. 1043–1127, 2002.
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[25]
2002 | Journal Article | IST-REx-ID: 2739
L. Erdös and V. Vougalter, “Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields,” Communications in Mathematical Physics, vol. 225, no. 2. Springer, pp. 399–421, 2002.
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[24]
2002 | Journal Article | IST-REx-ID: 2740
L. Erdös, “Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions,” Annales de l’Institut Fourier, vol. 52, no. 6. Association des Annales de l’Institut Fourier, p. 1833–1874+XI+VII, 2002.
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[23]
2001 | Journal Article | IST-REx-ID: 2709
L. Erdös, “Long time dynamics of an electron in a weakly coupled phonon field,” ICMP: International Congress on Mathematical Physics. World Scientific Publishing, pp. 273–281, 2001.
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[22]
2001 | Journal Article | IST-REx-ID: 2734
L. Erdös and J. Solovej, “The kernel of Dirac operators on S3 and R3,” Reviews in Mathematical Physics, vol. 13, no. 10. World Scientific Publishing, pp. 1247–1280, 2001.
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[21]
2001 | Journal Article | IST-REx-ID: 2735
L. Erdös, “Lifschitz tail in a magnetic field: Coexistence of classical and quantum behavior in the borderline case,” Probability Theory and Related Fields, vol. 121, no. 2. Springer, pp. 219–236, 2001.
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[20]
2001 | Journal Article | IST-REx-ID: 2736 | OA
L. Erdös and H. Yau, “Derivation of the nonlinear Schrödinger equation from a many body Coulomb system,” Advances in Theoretical and Mathematical Physics, vol. 5, no. 6. International Press, pp. 1169–1205, 2001.
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[19]
2000 | Conference Paper | IST-REx-ID: 2710
L. Erdös, “The kernel of Dirac operators on S3 and R3,” presented at the Differential Equations and Mathematical Physics, 2000, vol. 16, pp. 111–119.
View
 
[18]
2000 | Journal Article | IST-REx-ID: 2731
L. Erdös and H. Yau, “Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation,” Communications on Pure and Applied Mathematics, vol. 53, no. 6. Wiley-Blackwell, pp. 667–735, 2000.
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[17]
2000 | Journal Article | IST-REx-ID: 2732
F. Castella, L. Erdös, F. Frommlet, and P. Markowich, “Fokker-Planck equations as scaling limits of reversible quantum systems,” Journal of Statistical Physics, vol. 100, no. 3–4. Springer, pp. 543–601, 2000.
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[16]
2000 | Journal Article | IST-REx-ID: 2733
L. Erdös, M. Loss, and V. Vougalter, “Diamagnetic behavior of sums Dirichlet eigenvalues,” Annales de l’Institut Fourier, vol. 50, no. 3. Association des Annales de l’Institut Fourier, pp. 891–907, 2000.
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[15]
1999 | Conference Paper | IST-REx-ID: 2711
L. Erdös, “Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation,” presented at the QMath: Mathematical Results in Quantum Physics, 1999, vol. 108, pp. 233–242.
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[14]
1999 | Journal Article | IST-REx-ID: 2730
L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate,” Duke Mathematical Journal, vol. 96, no. 1. Duke University Press, pp. 127–173, 1999.
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[13]
1998 | Conference Paper | IST-REx-ID: 2695
L. Erdös and H. Yau, “Linear Boltzmann equation as scaling limit of quantum Lorentz gas,” presented at the Differential Equations and Mathematical Physics, 1998, vol. 217, pp. 137–155.
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[12]
1998 | Journal Article | IST-REx-ID: 2728
L. Erdös, “Lifschitz tail in a magnetic field: The nonclassical regime,” Probability Theory and Related Fields, vol. 112, no. 3. Springer, pp. 321–371, 1998.
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[11]
1997 | Journal Article | IST-REx-ID: 2727
L. Erdös, “Dia- and paramagnetism for nonhomogeneous magnetic fields,” Journal of Mathematical Physics, vol. 38, no. 3. American Institute of Physics, pp. 1289–1317, 1997.
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[10]
1997 | Journal Article | IST-REx-ID: 2729
L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates,” Communications in Mathematical Physics, vol. 188, no. 3. Springer, pp. 599–656, 1997.
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[9]
1996 | Journal Article | IST-REx-ID: 2725
L. Erdös, “Rayleigh-type isoperimetric inequality with a homogeneous magnetic field,” Calculus of Variations and Partial Differential Equations, vol. 4, no. 3. Springer, pp. 283–292, 1996.
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[8]
1996 | Journal Article | IST-REx-ID: 2726
L. Erdös, “Gaussian decay of the magnetic eigenfunctions,” Geometric and Functional Analysis, vol. 6, no. 2. Birkhäuser, pp. 231–248, 1996.
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[7]
1995 | Conference Paper | IST-REx-ID: 2712
L. Erdös, “Magnetic Lieb-Thirring inequalities and stochastic oscillatory integrals,” presented at the Partial Differential Operators and Mathematical Physics, 1995, vol. 78, pp. 127–132.
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[6]
1995 | Journal Article | IST-REx-ID: 2724
L. Erdös, “Magnetic Lieb-Thirring inequalities,” Communications in Mathematical Physics, vol. 170, no. 3. Springer, pp. 629–668, 1995.
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[5]
1994 | Journal Article | IST-REx-ID: 2713
L. Erdös, “Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator,” Duke Mathematical Journal, vol. 76, no. 2. Duke University Press, pp. 541–566, 1994.
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[4]
1993 | Journal Article | IST-REx-ID: 2723
L. Erdös, “Ground-state density of the Pauli operator in the large field limit,” Letters in Mathematical Physics, vol. 29, no. 3. Springer, pp. 219–240, 1993.
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[3]
1992 | Journal Article | IST-REx-ID: 2714
L. Erdös, “On some problems of P. Turán concerning power sums of complex numbers,” Acta Mathematica Hungarica, vol. 59, no. 1–2. Springer, pp. 11–24, 1992.
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[2]
1992 | Journal Article | IST-REx-ID: 2722
L. Erdös and D. Tuyen, “Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers,” Communications in Mathematical Physics, vol. 143, no. 3. Springer, pp. 451–466, 1992.
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[1]
1990 | Journal Article | IST-REx-ID: 2721
L. Erdös and D. Tuyen, “Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier,” Journal of Statistical Physics, vol. 59, no. 5–6. Springer, pp. 1589–1602, 1990.
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