119 Publications

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[119]
2019 | 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, 2019.
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[118]
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, pp. 1270–1334, 2019.
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[117]
2019 | Journal Article | IST-REx-ID: 6240
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, pp. 661–696, 2019.
View | Files available | DOI | Download (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, p. e8, 2019.
View | Files available | DOI | arXiv
 
[115]
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, pp. 3271–3290, 2018.
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[114]
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, pp. 148–203, 2018.
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[113]
2018 | Preprint | 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,” arXiv. .
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[112]
2018 | Preprint | 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,” arXiv. .
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[111]
2018 | 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, 2018.
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[110]
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, pp. 3255–3298, 2018.
View | Files available | DOI | Download (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, 2018.
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[108]
2018 | Preprint | IST-REx-ID: 6183
J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and  cusps,” arXiv:1804.07752. .
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[107]
2018 | Preprint | IST-REx-ID: 6184
J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” arXiv:1804.07744. .
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[106]
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, pp. 667–727, 2017.
View | Files available | DOI
 
[105]
2017 | Journal Article | IST-REx-ID: 1010
J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” Electronic Journal of Probability, vol. 22, p. 25, 2017.
View | Files available | DOI | arXiv
 
[104]
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, pp. 673–776, 2017.
View | Files available | DOI
 
[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: 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, pp. 1672–1705, 2017.
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[101]
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, pp. 251–291, 2017.
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[100]
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, pp. 947–990, 2017.
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[99]
2017 | Journal Article | IST-REx-ID: 1144
L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21, 2017.
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[98]
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, pp. 1606–1656, 2017.
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[97]
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, pp. 739–800, 2017.
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[96]
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, pp. 672–719, 2016.
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[95]
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, pp. 280–302, 2016.
View | Files available | DOI
 
[94]
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, pp. 1815–1881, 2016.
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[93]
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, pp. 1927–2036, 2015.
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[92]
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, pp. 709–799, 2015.
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[91]
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, pp. 1365–1416, 2015.
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[90]
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, pp. 441–464, 2014.
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[89]
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, 2014.
View | Files available | DOI
 
[88]
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, p. 33, 2014.
View | Files available | DOI
 
[87]
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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[86]
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, pp. 261–353, 2014.
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[85]
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, pp. 1127–1190, 2014.
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[84]
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, pp. 1837–1926, 2013.
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[83]
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, pp. 367–416, 2013.
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[82]
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, pp. 2279–2375, 2013.
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[81]
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, pp. 1–58, 2013.
View | Files available | DOI
 
[80]
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, pp. 2093–2113, 2013.
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[79]
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, pp. 1003–1032, 2013.
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[78]
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, pp. 671–730, 2012.
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[77]
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, 2012.
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[76]
2012 | Preprint | IST-REx-ID: 2696   OA
L. Erdös, “Universality for random matrices and log-gases,” ArXiv. ArXiv, 2012.
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[75]
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, 2012.
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[74]
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, 2012.
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[73]
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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[72]
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, pp. 341–407, 2012.
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[71]
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, pp. 847–882, 2012.
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[70]
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, pp. 1719–1731, 2012.
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[69]
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, pp. 507–542, 2012.
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[68]
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, pp. 1435–1515, 2012.
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[67]
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, pp. 377–414, 2012.
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[66]
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, pp. 1–46, 2012.
View | DOI
 
[65]
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, pp. 900–923, 2012.
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[64]
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, pp. 587–640, 2012.
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[63]
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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[62]
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, pp. 1227–1319, 2011.
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[61]
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, pp. 509–554, 2011.
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[60]
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, pp. 75–119, 2011.
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[59]
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, pp. 291–370, 2010.
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[58]
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, pp. 526–603, 2010.
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[57]
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, pp. 895–925, 2010.
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[56]
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, pp. 436–479, 2010.
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[55]
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, pp. 229–249, 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, pp. 667–674, 2010.
View
 
[53]
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, pp. 641–655, 2009.
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[52]
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, pp. 1099–1156, 2009.
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[51]
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, pp. 815–852, 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, pp. 1171–1210, 2009.
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[49]
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, pp. 859–870, 2009.
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[48]
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, pp. 211–277, 2008.
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[47]
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, pp. 301–328, 2008.
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[46]
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, 2008.
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[45]
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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[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, 2007.
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[42]
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, pp. 1–53, 2007.
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[41]
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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[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, 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, pp. 261–294, 2007.
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[38]
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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[37]
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, pp. 1659–1741, 2006.
View | DOI
 
[36]
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, pp. 265–283, 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, 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, pp. 669–743, 2005.
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[33]
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, pp. 671–741, 2004.
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[32]
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, pp. 1241–1273, 2004.
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[31]
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, pp. 475–506, 2004.
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[30]
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, pp. 367–380, 2004.
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[29]
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, pp. 399–421, 2002.
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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, pp. 515–520, 2002.
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[26]
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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[25]
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, pp. 1043–1127, 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, p. 1833–1874+XI+VII, 2002.
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[23]
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, pp. 1247–1280, 2001.
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[22]
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, pp. 273–281, 2001.
View
 
[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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, pp. 219–240, 1993.
View | DOI
 
[3]
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, pp. 451–466, 1992.
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[2]
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, pp. 11–24, 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, pp. 1589–1602, 1990.
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[119]
2019 | 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, 2019.
View | DOI | Download (ext.) | arXiv
 
[118]
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, pp. 1270–1334, 2019.
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[117]
2019 | Journal Article | IST-REx-ID: 6240
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, pp. 661–696, 2019.
View | Files available | DOI | Download (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, p. e8, 2019.
View | Files available | DOI | arXiv
 
[115]
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, pp. 3271–3290, 2018.
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[114]
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, pp. 148–203, 2018.
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[113]
2018 | Preprint | 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,” arXiv. .
View | Files available | Download (ext.) | arXiv
 
[112]
2018 | Preprint | 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,” arXiv. .
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[111]
2018 | 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, 2018.
View | Files available | DOI
 
[110]
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, pp. 3255–3298, 2018.
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[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, 2018.
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[108]
2018 | Preprint | IST-REx-ID: 6183
J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and  cusps,” arXiv:1804.07752. .
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[107]
2018 | Preprint | IST-REx-ID: 6184
J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” arXiv:1804.07744. .
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[106]
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, pp. 667–727, 2017.
View | Files available | DOI
 
[105]
2017 | Journal Article | IST-REx-ID: 1010
J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” Electronic Journal of Probability, vol. 22, p. 25, 2017.
View | Files available | DOI | arXiv
 
[104]
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, pp. 673–776, 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: 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, pp. 1672–1705, 2017.
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[101]
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, pp. 251–291, 2017.
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[100]
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, pp. 947–990, 2017.
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[99]
2017 | Journal Article | IST-REx-ID: 1144
L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21, 2017.
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[98]
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, pp. 1606–1656, 2017.
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[97]
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, pp. 739–800, 2017.
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[96]
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, pp. 672–719, 2016.
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[95]
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, pp. 280–302, 2016.
View | Files available | DOI
 
[94]
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, pp. 1815–1881, 2016.
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[93]
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, pp. 1927–2036, 2015.
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[92]
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, pp. 709–799, 2015.
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[91]
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, pp. 1365–1416, 2015.
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[90]
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, pp. 441–464, 2014.
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[89]
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, 2014.
View | Files available | DOI
 
[88]
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, p. 33, 2014.
View | Files available | DOI
 
[87]
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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[86]
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, pp. 261–353, 2014.
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[85]
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, pp. 1127–1190, 2014.
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[84]
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, pp. 1837–1926, 2013.
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[83]
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, pp. 367–416, 2013.
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[82]
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, pp. 2279–2375, 2013.
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[81]
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, pp. 1–58, 2013.
View | Files available | DOI
 
[80]
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, pp. 2093–2113, 2013.
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[79]
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, pp. 1003–1032, 2013.
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[78]
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, pp. 671–730, 2012.
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[77]
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, 2012.
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[76]
2012 | Preprint | IST-REx-ID: 2696   OA
L. Erdös, “Universality for random matrices and log-gases,” ArXiv. ArXiv, 2012.
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[75]
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, 2012.
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[74]
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, 2012.
View | DOI
 
[73]
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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[72]
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, pp. 341–407, 2012.
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[71]
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, pp. 847–882, 2012.
View | DOI
 
[70]
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, pp. 1719–1731, 2012.
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[69]
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, pp. 507–542, 2012.
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[68]
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, pp. 1435–1515, 2012.
View | DOI
 
[67]
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, pp. 377–414, 2012.
View | DOI
 
[66]
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, pp. 1–46, 2012.
View | DOI
 
[65]
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, pp. 900–923, 2012.
View | DOI
 
[64]
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, pp. 587–640, 2012.
View | DOI
 
[63]
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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[62]
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, pp. 1227–1319, 2011.
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[61]
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, pp. 509–554, 2011.
View | DOI
 
[60]
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, pp. 75–119, 2011.
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[59]
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, pp. 291–370, 2010.
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[58]
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, pp. 526–603, 2010.
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[57]
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, pp. 895–925, 2010.
View | DOI
 
[56]
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, pp. 436–479, 2010.
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[55]
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, pp. 229–249, 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, pp. 667–674, 2010.
View
 
[53]
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, pp. 641–655, 2009.
View | DOI
 
[52]
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, pp. 1099–1156, 2009.
View | DOI
 
[51]
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, pp. 815–852, 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, pp. 1171–1210, 2009.
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[49]
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, pp. 859–870, 2009.
View | DOI
 
[48]
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, pp. 211–277, 2008.
View | DOI
 
[47]
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, pp. 301–328, 2008.
View | DOI
 
[46]
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, 2008.
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[45]
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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[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, 2007.
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[42]
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, pp. 1–53, 2007.
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[41]
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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[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, 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, pp. 261–294, 2007.
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[38]
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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[37]
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, pp. 1659–1741, 2006.
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[36]
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, pp. 265–283, 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, 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, pp. 669–743, 2005.
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[33]
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, pp. 671–741, 2004.
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[32]
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, pp. 1241–1273, 2004.
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[31]
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, pp. 475–506, 2004.
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[30]
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, pp. 367–380, 2004.
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[29]
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, pp. 399–421, 2002.
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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, pp. 515–520, 2002.
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[26]
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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[25]
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, pp. 1043–1127, 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, p. 1833–1874+XI+VII, 2002.
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[23]
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, pp. 1247–1280, 2001.
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[22]
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, pp. 273–281, 2001.
View
 
[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, 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, 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, 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, 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, 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, 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.
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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, 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, 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, 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, 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, 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.
View | DOI
 
[6]
1995 | Journal Article | IST-REx-ID: 2724
L. Erdös, “Magnetic Lieb-Thirring inequalities,” Communications in Mathematical Physics, vol. 170, no. 3, 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, 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, pp. 219–240, 1993.
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[3]
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, pp. 451–466, 1992.
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[2]
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, pp. 11–24, 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, pp. 1589–1602, 1990.
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