119 Publications

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[119]
2019 | Journal Article | IST-REx-ID: 6488   OA
Cipolloni, G., & Erdös, L. (2019). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. https://doi.org/10.1142/S2010326320500069
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[118]
2019 | Journal Article | IST-REx-ID: 6511   OA
Bao, Z., Erdös, L., & Schnelli, K. (2019). Local single ring theorem on optimal scale. Annals of Probability, 47(3), 1270–1334. https://doi.org/10.1214/18-AOP1284
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[117]
2019 | Journal Article | IST-REx-ID: 6240
Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare, 55(2), 661–696. https://doi.org/10.1214/18-AIHP894
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[116]
2019 | Journal Article | IST-REx-ID: 6182   OA
Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma, 7, e8. https://doi.org/10.1017/fms.2019.2
View | Files available | DOI | arXiv
 
[115]
2018 | Journal Article | IST-REx-ID: 181   OA
Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis, 50(3), 3271–3290. https://doi.org/10.1137/17M1143125
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[114]
2018 | Journal Article | IST-REx-ID: 566   OA
Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular law. Annals Applied Probability , 28(1), 148–203. https://doi.org/10.1214/17-AAP1302
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[113]
2018 | Preprint | IST-REx-ID: 6185   OA
Erdös, L., Krüger, T. H., & Schröder, D. J. (n.d.). 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
Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (n.d.). Cusp universality for random matrices II: The real symmetric case. ArXiv.
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[111]
2018 | Journal Article | IST-REx-ID: 429   OA
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2018). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. https://doi.org/10.1007/s00440-018-0835-z
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[110]
2018 | Journal Article | IST-REx-ID: 1012   OA
Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices, 2018(10), 3255–3298. https://doi.org/10.1093/imrn/rnw330
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[109]
2018 | Journal Article | IST-REx-ID: 5971   OA
Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. https://doi.org/10.1142/s2010326319500096
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[108]
2018 | Preprint | IST-REx-ID: 6183
Alt, J., Erdös, L., & Krüger, T. H. (n.d.). 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
Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (n.d.). Correlated random matrices: Band rigidity and edge universality. ArXiv:1804.07744.
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[106]
2017 | Journal Article | IST-REx-ID: 1337   OA
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2017). Universality for general Wigner-type matrices. Probability Theory and Related Fields, 169(3–4), 667–727. https://doi.org/10.1007/s00440-016-0740-2
View | Files available | DOI
 
[105]
2017 | Journal Article | IST-REx-ID: 1010
Alt, J., Erdös, L., & Krüger, T. H. (2017). Local law for random Gram matrices. Electronic Journal of Probability, 22, 25. https://doi.org/10.1214/17-EJP42
View | Files available | DOI | arXiv
 
[104]
2017 | Journal Article | IST-REx-ID: 1528   OA
Bao, Z., & Erdös, L. (2017). Delocalization for a class of random block band matrices. Probability Theory and Related Fields, 167(3–4), 673–776. https://doi.org/10.1007/s00440-015-0692-y
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[103]
2017 | Book | IST-REx-ID: 567
Erdös, L., & Yau, H. (2017). A dynamical approach to random matrix theory (Vol. 28). American Mathematical Society.
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[102]
2017 | Journal Article | IST-REx-ID: 721   OA
Ajanki, O. H., Krüger, T. H., & Erdös, L. (2017). Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics, 70(9), 1672–1705. https://doi.org/10.1002/cpa.21639
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[101]
2017 | Journal Article | IST-REx-ID: 733   OA
Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics, 319, 251–291. https://doi.org/10.1016/j.aim.2017.08.028
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[100]
2017 | Journal Article | IST-REx-ID: 1207   OA
Bao, Z., Erdös, L., & Schnelli, K. (2017). Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics, 349(3), 947–990. https://doi.org/10.1007/s00220-016-2805-6
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[99]
2017 | Journal Article | IST-REx-ID: 1144
Erdös, L., & Schröder, D. J. (2017). Fluctuations of functions of Wigner matrices. Electronic Communications in Probability, 21. https://doi.org/10.1214/16-ECP38
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[98]
2017 | Journal Article | IST-REx-ID: 615   OA
Erdös, L., & Schnelli, K. (2017). Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics, 53(4), 1606–1656. https://doi.org/10.1214/16-AIHP765
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[97]
2017 | Journal Article | IST-REx-ID: 483   OA
Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics, 21(3), 739–800. https://doi.org/10.4310/ATMP.2017.v21.n3.a5
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[96]
2016 | Journal Article | IST-REx-ID: 1434   OA
Bao, Z., Erdös, L., & Schnelli, K. (2016). Local stability of the free additive convolution. Journal of Functional Analysis, 271(3), 672–719. https://doi.org/10.1016/j.jfa.2016.04.006
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[95]
2016 | Journal Article | IST-REx-ID: 1489   OA
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2016). Local spectral statistics of Gaussian matrices with correlated entries. Journal of Statistical Physics, 163(2), 280–302. https://doi.org/10.1007/s10955-016-1479-y
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[94]
2016 | Journal Article | IST-REx-ID: 1280   OA
Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2016). Fixed energy universality for generalized wigner matrices. Communications on Pure and Applied Mathematics, 69(10), 1815–1881. https://doi.org/10.1002/cpa.21624
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[93]
2015 | Journal Article | IST-REx-ID: 1508   OA
Erdös, L., & Yau, H. (2015). Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society, 17(8), 1927–2036. https://doi.org/10.4171/JEMS/548
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[92]
2015 | Journal Article | IST-REx-ID: 1864   OA
Erdös, L., & Knowles, A. (2015). The Altshuler–Shklovskii formulas for random band matrices II: The general case. Annales Henri Poincare, 16(3), 709–799. https://doi.org/10.1007/s00023-014-0333-5
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[91]
2015 | Journal Article | IST-REx-ID: 2166   OA
Erdös, L., & Knowles, A. (2015). The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Communications in Mathematical Physics, 333(3), 1365–1416. https://doi.org/10.1007/s00220-014-2119-5
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[90]
2014 | Journal Article | IST-REx-ID: 2019   OA
Erdös, L., & Schröder, D. J. (2014). Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry, 17(3–4), 441–464. https://doi.org/10.1007/s11040-014-9164-3
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[89]
2014 | Journal Article | IST-REx-ID: 2179   OA
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2014). Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability, 19. https://doi.org/10.1214/ECP.v19-3121
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[88]
2014 | Journal Article | IST-REx-ID: 2225   OA
Bloemendal, A., Erdös, L., Knowles, A., Yau, H., & Yin, J. (2014). Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability, 19, 33. https://doi.org/10.1214/EJP.v19-3054
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[87]
2014 | Conference Paper | IST-REx-ID: 1507   OA
Erdös, L. (2014). Random matrices, log-gases and Hölder regularity (Vol. 3, pp. 214–236). Presented at the ICM: International Congress of Mathematicians, Seoul, Korea: Kyung Moon SA Co. Ltd.
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[86]
2014 | Journal Article | IST-REx-ID: 1937   OA
Bourgade, P., Erdös, L., & Yau, H. (2014). Edge universality of beta ensembles. Communications in Mathematical Physics, 332(1), 261–353. https://doi.org/10.1007/s00220-014-2120-z
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[85]
2014 | Journal Article | IST-REx-ID: 2699   OA
Erdös, L., Bourgade, P., & Yau, H. (2014). Universality of general β-ensembles. Duke Mathematical Journal, 163(6), 1127–1190. https://doi.org/10.1215/00127094-2649752
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[84]
2013 | Journal Article | IST-REx-ID: 2780   OA
Erdös, L., Knowles, A., & Yau, H. (2013). Averaging fluctuations in resolvents of random band matrices. Annales Henri Poincare, 14(8), 1837–1926. https://doi.org/10.1007/s00023-013-0235-y
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[83]
2013 | Journal Article | IST-REx-ID: 2697   OA
Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). Delocalization and diffusion profile for random band matrices. Communications in Mathematical Physics, 323(1), 367–416. https://doi.org/10.1007/s00220-013-1773-3
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[82]
2013 | Journal Article | IST-REx-ID: 2781   OA
Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). Spectral statistics of Erdős-Rényi graphs I: Local semicircle law. Annals of Probability, 41(3 B), 2279–2375. https://doi.org/10.1214/11-AOP734
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[81]
2013 | Journal Article | IST-REx-ID: 2837   OA
Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). The local semicircle law for a general class of random matrices. Electronic Journal of Probability, 18(59), 1–58. https://doi.org/10.1214/EJP.v18-2473
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[80]
2013 | Journal Article | IST-REx-ID: 2698   OA
Erdös, L., Fournais, S., & Solovej, J. (2013). Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society, 15(6), 2093–2113. https://doi.org/10.4171/JEMS/416
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[79]
2013 | Journal Article | IST-REx-ID: 2782   OA
Erdös, L., & Farrell, B. (2013). Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics, 152(6), 1003–1032. https://doi.org/10.1007/s10955-013-0807-8
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[78]
2012 | Journal Article | IST-REx-ID: 2772
Erdös, L., Fournais, S., & Solovej, J. (2012). Second order semiclassics with self generated magnetic fields. Annales Henri Poincare, 13(4), 671–730. https://doi.org/10.1007/s00023-011-0150-z
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[77]
2012 | Journal Article | IST-REx-ID: 2777
Erdös, L., Fournais, S., & Solovej, J. (2012). Relativistic Scott correction in self-generated magnetic fields. Journal of Mathematical Physics, 53(9). https://doi.org/10.1063/1.3697417
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[76]
2012 | Preprint | IST-REx-ID: 2696   OA
Erdös, L. (2012). Universality for random matrices and log-gases. ArXiv. ArXiv.
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[75]
2012 | Journal Article | IST-REx-ID: 2773
Erdös, L., & Yau, H. (2012). A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability, 17. https://doi.org/10.1214/EJP.v17-1779
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[74]
2012 | Journal Article | IST-REx-ID: 2778
Bourgade, P., Erdös, L., & Yau, H. (2012). Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics, 53(9). https://doi.org/10.1063/1.4751478
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[73]
2012 | Conference Paper | IST-REx-ID: 2700   OA
Erdös, L. (2012). Lecture notes on quantum Brownian motion (Vol. 95, pp. 3–98). Presented at the Les Houches Summer School 2010, Oxford University Press.
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[72]
2012 | Journal Article | IST-REx-ID: 2767
Erdös, L., Yau, H., & Yin, J. (2012). Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields, 154(1–2), 341–407. https://doi.org/10.1007/s00440-011-0390-3
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[71]
2012 | Journal Article | IST-REx-ID: 2774
Erdös, L., Fournais, S., & Solovej, J. (2012). Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics, 312(3), 847–882. https://doi.org/10.1007/s00220-012-1468-1
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[70]
2012 | Journal Article | IST-REx-ID: 2779
Erdös, L., & Hasler, D. (2012). Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare, 13(8), 1719–1731. https://doi.org/10.1007/s00023-012-0177-9
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[69]
2012 | Journal Article | IST-REx-ID: 2768
Erdös, L., & Hasler, D. (2012). Wegner estimate and Anderson localization for random magnetic fields. Communications in Mathematical Physics, 309(2), 507–542. https://doi.org/10.1007/s00220-011-1373-z
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[68]
2012 | Journal Article | IST-REx-ID: 2770
Erdös, L., Yau, H., & Yin, J. (2012). Rigidity of eigenvalues of generalized Wigner matrices. Advances in Mathematics, 229(3), 1435–1515. https://doi.org/10.1016/j.aim.2011.12.010
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[67]
2012 | Journal Article | IST-REx-ID: 2775
Erdös, L., & Yau, H. (2012). Universality of local spectral statistics of random matrices. Bulletin of the American Mathematical Society, 49(3), 377–414. https://doi.org/10.1090/S0273-0979-2012-01372-1
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[66]
2012 | Journal Article | IST-REx-ID: 2769
Erdös, L., Schlein, B., Yau, H., & Yin, J. (2012). The local relaxation flow approach to universality of the local statistics for random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics, 48(1), 1–46. https://doi.org/10.1214/10-AIHP388
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[65]
2012 | Journal Article | IST-REx-ID: 2771
Erdös, L., & Hasler, D. (2012). Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics, 146(5), 900–923. https://doi.org/10.1007/s10955-012-0445-6
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[64]
2012 | Journal Article | IST-REx-ID: 2776
Erdös, L., Knowles, A., Yau, H., & Yin, J. (2012). Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical Physics, 314(3), 587–640. https://doi.org/10.1007/s00220-012-1527-7
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[63]
2011 | Book Review | IST-REx-ID: 2765
Erdös, L. (2011). Universality of Wigner random matrices: A survey of recent results. Russian Mathematical Surveys. IOP Publishing Ltd. https://doi.org/10.1070/RM2011v066n03ABEH004749
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[62]
2011 | Journal Article | IST-REx-ID: 2766
Erdös, L., & Knowles, A. (2011). Quantum diffusion and delocalization for band matrices with general distribution. Annales Henri Poincare, 12(7), 1227–1319. https://doi.org/10.1007/s00023-011-0104-5
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[61]
2011 | Journal Article | IST-REx-ID: 2717
Erdös, L., & Knowles, A. (2011). Quantum diffusion and eigenfunction delocalization in a random band matrix model. Communications in Mathematical Physics, 303(2), 509–554. https://doi.org/10.1007/s00220-011-1204-2
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[60]
2011 | Journal Article | IST-REx-ID: 2764
Erdös, L., Schlein, B., & Yau, H. (2011). Universality of random matrices and local relaxation flow. Inventiones Mathematicae, 185(1), 75–119. https://doi.org/10.1007/s00222-010-0302-7
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[59]
2010 | Journal Article | IST-REx-ID: 2704
Erdös, L., Schlein, B., & Yau, H. (2010). Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate. Annals of Mathematics, 172(1), 291–370. https://doi.org/10.4007/annals.2010.172.291
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[58]
2010 | Journal Article | IST-REx-ID: 2761
Erdös, L., Ramírez, J., Schlein, B., & Yau, H. (2010). Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation. Electronic Journal of Probability, 15(18), 526–603. https://doi.org/10.1214/EJP.v15-768
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[57]
2010 | Journal Article | IST-REx-ID: 2762
Erdös, L., Ramírez, J., Yau, H., Péché, S., & Schlein, B. (2010). Bulk universality for Wigner matrices. Communications on Pure and Applied Mathematics, 63(7), 895–925. https://doi.org/10.1002/cpa.20317
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[56]
2010 | Journal Article | IST-REx-ID: 2701   OA
Erdös, L., Schlein, B., & Yau, H. (2010). Wegner estimate and level repulsion for Wigner random matrices. International Mathematics Research Notices, (3), 436–479. https://doi.org/10.1093/imrn/rnp136
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[55]
2010 | Journal Article | IST-REx-ID: 2756
Erdös, L., & Solovej, J. (2010). Ground state energy of large atoms in a self-generated magnetic field. Communications in Mathematical Physics, 294(1), 229–249. https://doi.org/10.1007/s00220-009-0869-2
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[54]
2010 | Journal Article | IST-REx-ID: 2763
Erdös, L., Ramírez, J., Schlein, B., Tao, T., Van, V., & Yau, H. (2010). Bulk universality for Wigner Hermitian matrices with subexponential decay. Mathematical Research Letters, 17(4), 667–674.
View
 
[53]
2009 | Journal Article | IST-REx-ID: 2758
Erdös, L., Schlein, B., & Yau, H. (2009). Local semicircle law and complete delocalization for Wigner random matrices. Communications in Mathematical Physics, 287(2), 641–655. https://doi.org/10.1007/s00220-008-0636-9
View | DOI
 
[52]
2009 | Journal Article | IST-REx-ID: 2760
Erdös, L., Schlein, B., & Yau, H. (2009). Rigorous derivation of the gross-pitaevskii equation with a large interaction potential. Journal of the American Mathematical Society, 22(4), 1099–1156. https://doi.org/10.1090/S0894-0347-09-00635-3
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[51]
2009 | Journal Article | IST-REx-ID: 2703
Erdös, L., Schlein, B., & Yau, H. (2009). Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices. Annals of Probability, 37(3), 815–852. https://doi.org/10.1214/08-AOP421
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[50]
2009 | Journal Article | IST-REx-ID: 2759
Erdös, L., Michelangeli, A., & Schlein, B. (2009). Dynamical formation of correlations in a Bose-Einstein condensate. Communications in Mathematical Physics, 289(3), 1171–1210. https://doi.org/10.1007/s00220-009-0828-y
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[49]
2009 | Journal Article | IST-REx-ID: 2757
Erdös, L., & Schlein, B. (2009). Quantum dynamics with mean field interactions: A new approach. Journal of Statistical Physics, 134(5–6), 859–870. https://doi.org/10.1007/s10955-008-9570-7
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[48]
2008 | Journal Article | IST-REx-ID: 2753
Erdös, L., Salmhofer, M., & Yau, H. (2008). Quantum diffusion of the random Schrödinger evolution in the scaling limit. Acta Mathematica, 200(2), 211–277. https://doi.org/10.1007/s11511-008-0027-2
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[47]
2008 | Journal Article | IST-REx-ID: 2754
Adami, R., & Erdös, L. (2008). Rate of decoherence for an electron weakly coupled to a phonon gas. Journal of Statistical Physics, 132(2), 301–328. https://doi.org/10.1007/s10955-008-9561-8
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[46]
2008 | Journal Article | IST-REx-ID: 2755
Erdös, L., Schlein, B., & Yau, H. (2008). Ground-state energy of a low-density Bose gas: A second-order upper bound. Physical Review A - Atomic, Molecular, and Optical Physics, 78(5). https://doi.org/10.1103/PhysRevA.78.053627
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[45]
2008 | Conference Paper | IST-REx-ID: 2702   OA
Erdös, L., Salmhofer, M., & Yau, H. (2008). Feynman graphs and renormalization in quantum diffusion (pp. 167–182). Presented at the Symposium in Honor of Wolfhart Zimmermann’s 80th Birthday, World Scientific Publishing. https://doi.org/10.1142/9789812833556_0011
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[44]
2007 | Book Chapter | IST-REx-ID: 2705   OA
Erdös, L. (2007). Recent developments in quantum mechanics with magnetic fields. In F. Gesztesy, P. Deift, P. Galvez, P. Perry, & W. Schlag (Eds.), Spectral Theory and Mathematical Physics: a Festschrift in Honor of Barry Simon’s 60th Birthday (Vol. 76, pp. 401–428). American Mathematical Society.
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[43]
2007 | Journal Article | IST-REx-ID: 2748
Erdös, L., Schlein, B., & Yau, H. (2007). Rigorous derivation of the Gross-Pitaevskii equation. Physical Review Letters, 98(4). https://doi.org/10.1103/PhysRevLett.98.040404
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[42]
2007 | Journal Article | IST-REx-ID: 2750
Erdös, L., Salmhofer, M., & Yau, H. (2007). Quantum diffusion of the random Schrödinger evolution in the scaling limit II. The recollision diagrams. Communications in Mathematical Physics, 271(1), 1–53. https://doi.org/10.1007/s00220-006-0158-2
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[41]
2007 | Book Review | IST-REx-ID: 2749
Erdös, L., Schlein, B., & Yau, H. (2007). Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-006-0022-1
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[40]
2007 | Journal Article | IST-REx-ID: 2751
Erdös, L., Salmhofer, M., & Yau, H. (2007). Quantum diffusion for the Anderson model in the scaling limit. Annales Henri Poincare, 8(4), 621–685. https://doi.org/10.1007/s00023-006-0318-0
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[39]
2007 | Journal Article | IST-REx-ID: 2752
Erdös, L., & Salmhofer, M. (2007). Decay of the Fourier transform of surfaces with vanishing curvature. Mathematische Zeitschrift, 257(2), 261–294. https://doi.org/10.1007/s00209-007-0125-4
View | DOI
 
[38]
2006 | Conference Paper | IST-REx-ID: 2746
Erdös, L., Salmhofer, M., & Yau, H. (2006). Towards the quantum Brownian motion (Vol. 690, pp. 233–257). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. https://doi.org/10.1007/3-540-34273-7_18
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[37]
2006 | Journal Article | IST-REx-ID: 2747
Erdös, L., Schlein, B., & Yau, H. (2006). Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate. Communications on Pure and Applied Mathematics, 59(12), 1659–1741. https://doi.org/10.1002/cpa.20123
View | DOI
 
[36]
2006 | Journal Article | IST-REx-ID: 2745
Elgart, A., Erdös, L., Schlein, B., & Yau, H. (2006). Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons. Archive for Rational Mechanics and Analysis, 179(2), 265–283. https://doi.org/10.1007/s00205-005-0388-z
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[35]
2005 | Journal Article | IST-REx-ID: 2743
Erdös, L., Hasler, D., & Solovej, J. (2005). Existence of the D0-D4 bound state: A detailed proof. Annales Henri Poincare, 6(2), 247–267. https://doi.org/10.1007/s00023-005-0205-0
View | DOI
 
[34]
2005 | Journal Article | IST-REx-ID: 2744
Eng, D., & Erdös, L. (2005). The linear Boltzmann equation as the low density limit of a random Schrödinger equation. Reviews in Mathematical Physics, 17(6), 669–743. https://doi.org/10.1142/S0129055X0500242X
View | DOI
 
[33]
2004 | Journal Article | IST-REx-ID: 2741
Erdös, L., & Solovej, J. (2004). Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field. Annales Henri Poincare, 5(4), 671–741. https://doi.org/10.1007/s00023-004-0180-x
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[32]
2004 | Journal Article | IST-REx-ID: 2742
Elgart, A., Erdös, L., Schlein, B., & Yau, H. (2004). Nonlinear Hartree equation as the mean field limit of weakly coupled fermions. Journal de Mathématiques Pures et Appliquées, 83(10), 1241–1273. https://doi.org/10.1016/j.matpur.2004.03.006
View | DOI
 
[31]
2004 | Journal Article | IST-REx-ID: 2706
Erdös, L., & Solovej, J. (2004). Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength. Journal of Statistical Physics, 116(1–4), 475–506. https://doi.org/10.1023/B:JOSS.0000037216.45270.1d
View | DOI
 
[30]
2004 | Journal Article | IST-REx-ID: 2707
Erdös, L., Salmhofer, M., & Yau, H. (2004). On the quantum Boltzmann equation. Journal of Statistical Physics, 116(1–4), 367–380. https://doi.org/10.1023/B:JOSS.0000037224.56191.ed
View | DOI
 
[29]
2002 | Journal Article | IST-REx-ID: 2739
Erdös, L., & Vougalter, V. (2002). Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields. Communications in Mathematical Physics, 225(2), 399–421. https://doi.org/10.1007/s002200100585
View | DOI
 
[28]
2002 | Conference Paper | IST-REx-ID: 2708
Erdös, L. (2002). Two dimensional Pauli operator via scalar potential (Vol. 307, pp. 129–133). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. https://doi.org/10.1090/conm/307
View | DOI
 
[27]
2002 | Journal Article | IST-REx-ID: 2737
Bardos, C., Erdös, L., Golse, F., Mauser, N., & Yau, H. (2002). Derivation of the Schrödinger-Poisson equation from the quantum N-body problem. Comptes Rendus Mathematique, 334(6), 515–520. https://doi.org/10.1016/S1631-073X(02)02253-7
View | DOI
 
[26]
2002 | Conference Paper | IST-REx-ID: 2694
Erdös, L. (2002). Scaling limits of Schrödinger quantum mechanics (Vol. 597, pp. 487–506). Presented at the 38th Winter School of Theoretical Physics : Dynamical Semigroups: Dissipation, Chaos, Quanta, Springer. https://doi.org/10.1007/3-540-46122-1_19
View | DOI
 
[25]
2002 | Journal Article | IST-REx-ID: 2738
Erdös, L. (2002). Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics, 107(5–6), 1043–1127. https://doi.org/10.1023/A:1015157624384
View | DOI
 
[24]
2002 | Journal Article | IST-REx-ID: 2740
Erdös, L. (2002). Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions. Annales de l’Institut Fourier, 52(6), 1833–1874+XI+VII. https://doi.org/10.5802/aif.1936
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[23]
2001 | Journal Article | IST-REx-ID: 2734
Erdös, L., & Solovej, J. (2001). The kernel of Dirac operators on S3 and R3. Reviews in Mathematical Physics, 13(10), 1247–1280. https://doi.org/10.1142/S0129055X01000983
View | DOI
 
[22]
2001 | Journal Article | IST-REx-ID: 2709
Erdös, L. (2001). Long time dynamics of an electron in a weakly coupled phonon field. ICMP: International Congress on Mathematical Physics, 273–281.
View
 
[21]
2001 | Journal Article | IST-REx-ID: 2735
Erdös, L. (2001). Lifschitz tail in a magnetic field: Coexistence of classical and quantum behavior in the borderline case. Probability Theory and Related Fields, 121(2), 219–236. https://doi.org/10.1007/PL00008803
View | DOI
 
[20]
2001 | Journal Article | IST-REx-ID: 2736   OA
Erdös, L., & Yau, H. (2001). Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Advances in Theoretical and Mathematical Physics, 5(6), 1169–1205.
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[19]
2000 | Conference Paper | IST-REx-ID: 2710
Erdös, L. (2000). The kernel of Dirac operators on S3 and R3 (Vol. 16, pp. 111–119). Presented at the Differential Equations and Mathematical Physics, American Mathematical Society.
View
 
[18]
2000 | Journal Article | IST-REx-ID: 2731
Erdös, L., & Yau, H. (2000). Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation. Communications on Pure and Applied Mathematics, 53(6), 667–735. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5
View | DOI
 
[17]
2000 | Journal Article | IST-REx-ID: 2732
Castella, F., Erdös, L., Frommlet, F., & Markowich, P. (2000). Fokker-Planck equations as scaling limits of reversible quantum systems. Journal of Statistical Physics, 100(3–4), 543–601. https://doi.org/10.1023/A:1018667323830
View | DOI
 
[16]
2000 | Journal Article | IST-REx-ID: 2733
Erdös, L., Loss, M., & Vougalter, V. (2000). Diamagnetic behavior of sums Dirichlet eigenvalues. Annales de l’Institut Fourier, 50(3), 891–907. https://doi.org/10.5802/aif.1777
View | DOI
 
[15]
1999 | Conference Paper | IST-REx-ID: 2711
Erdös, L. (1999). Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation (Vol. 108, pp. 233–242). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. https://doi.org/10.1007/978-3-0348-8745-8_20
View | DOI
 
[14]
1999 | Journal Article | IST-REx-ID: 2730
Erdös, L., & Solovej, J. (1999). Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. Duke Mathematical Journal, 96(1), 127–173. https://doi.org/10.1215/S0012-7094-99-09604-7
View | DOI
 
[13]
1998 | Conference Paper | IST-REx-ID: 2695
Erdös, L., & Yau, H. (1998). Linear Boltzmann equation as scaling limit of quantum Lorentz gas (Vol. 217, pp. 137–155). Presented at the Differential Equations and Mathematical Physics, American Mathematical Society. https://doi.org/10.1090/conm/217
View | DOI
 
[12]
1998 | Journal Article | IST-REx-ID: 2728
Erdös, L. (1998). Lifschitz tail in a magnetic field: The nonclassical regime. Probability Theory and Related Fields, 112(3), 321–371. https://doi.org/10.1007/s004400050193
View | DOI
 
[11]
1997 | Journal Article | IST-REx-ID: 2727
Erdös, L. (1997). Dia- and paramagnetism for nonhomogeneous magnetic fields. Journal of Mathematical Physics, 38(3), 1289–1317. https://doi.org/10.1063/1.531909
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[10]
1997 | Journal Article | IST-REx-ID: 2729
Erdös, L., & Solovej, J. (1997). Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates. Communications in Mathematical Physics, 188(3), 599–656. https://doi.org/10.1007/s002200050181
View | DOI
 
[9]
1996 | Journal Article | IST-REx-ID: 2725
Erdös, L. (1996). Rayleigh-type isoperimetric inequality with a homogeneous magnetic field. Calculus of Variations and Partial Differential Equations, 4(3), 283–292. https://doi.org/10.1007/BF01254348
View | DOI
 
[8]
1996 | Journal Article | IST-REx-ID: 2726
Erdös, L. (1996). Gaussian decay of the magnetic eigenfunctions. Geometric and Functional Analysis, 6(2), 231–248. https://doi.org/10.1007/BF02247886
View | DOI
 
[7]
1995 | Conference Paper | IST-REx-ID: 2712
Erdös, L. (1995). Magnetic Lieb-Thirring inequalities and stochastic oscillatory integrals (Vol. 78, pp. 127–132). Presented at the Partial Differential Operators and Mathematical Physics, Birkhäuser. https://doi.org/10.1007/978-3-0348-9092-2_13
View | DOI
 
[6]
1995 | Journal Article | IST-REx-ID: 2724
Erdös, L. (1995). Magnetic Lieb-Thirring inequalities. Communications in Mathematical Physics, 170(3), 629–668. https://doi.org/10.1007/BF02099152
View | DOI
 
[5]
1994 | Journal Article | IST-REx-ID: 2713
Erdös, L. (1994). Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator. Duke Mathematical Journal, 76(2), 541–566. https://doi.org/10.1215/S0012-7094-94-07619-9
View | DOI
 
[4]
1993 | Journal Article | IST-REx-ID: 2723
Erdös, L. (1993). Ground-state density of the Pauli operator in the large field limit. Letters in Mathematical Physics, 29(3), 219–240. https://doi.org/10.1007/BF00761110
View | DOI
 
[3]
1992 | Journal Article | IST-REx-ID: 2722
Erdös, L., & Tuyen, D. (1992). Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers. Communications in Mathematical Physics, 143(3), 451–466. https://doi.org/10.1007/BF02099260
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[2]
1992 | Journal Article | IST-REx-ID: 2714
Erdös, L. (1992). On some problems of P. Turán concerning power sums of complex numbers. Acta Mathematica Hungarica, 59(1–2), 11–24. https://doi.org/10.1007/BF00052086
View | DOI
 
[1]
1990 | Journal Article | IST-REx-ID: 2721
Erdös, L., & Tuyen, D. (1990). Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier. Journal of Statistical Physics, 59(5–6), 1589–1602. https://doi.org/10.1007/BF01334766
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[119]
2019 | Journal Article | IST-REx-ID: 6488   OA
Cipolloni, G., & Erdös, L. (2019). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. https://doi.org/10.1142/S2010326320500069
View | DOI | Download (ext.) | arXiv
 
[118]
2019 | Journal Article | IST-REx-ID: 6511   OA
Bao, Z., Erdös, L., & Schnelli, K. (2019). Local single ring theorem on optimal scale. Annals of Probability, 47(3), 1270–1334. https://doi.org/10.1214/18-AOP1284
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[117]
2019 | Journal Article | IST-REx-ID: 6240
Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare, 55(2), 661–696. https://doi.org/10.1214/18-AIHP894
View | Files available | DOI | Download (ext.) | arXiv
 
[116]
2019 | Journal Article | IST-REx-ID: 6182   OA
Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma, 7, e8. https://doi.org/10.1017/fms.2019.2
View | Files available | DOI | arXiv
 
[115]
2018 | Journal Article | IST-REx-ID: 181   OA
Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis, 50(3), 3271–3290. https://doi.org/10.1137/17M1143125
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[114]
2018 | Journal Article | IST-REx-ID: 566   OA
Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular law. Annals Applied Probability , 28(1), 148–203. https://doi.org/10.1214/17-AAP1302
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[113]
2018 | Preprint | IST-REx-ID: 6185   OA
Erdös, L., Krüger, T. H., & Schröder, D. J. (n.d.). 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
Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (n.d.). Cusp universality for random matrices II: The real symmetric case. ArXiv.
View | Files available | Download (ext.) | arXiv
 
[111]
2018 | Journal Article | IST-REx-ID: 429   OA
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2018). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. https://doi.org/10.1007/s00440-018-0835-z
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[110]
2018 | Journal Article | IST-REx-ID: 1012   OA
Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices, 2018(10), 3255–3298. https://doi.org/10.1093/imrn/rnw330
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[109]
2018 | Journal Article | IST-REx-ID: 5971   OA
Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. https://doi.org/10.1142/s2010326319500096
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[108]
2018 | Preprint | IST-REx-ID: 6183
Alt, J., Erdös, L., & Krüger, T. H. (n.d.). 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
Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (n.d.). Correlated random matrices: Band rigidity and edge universality. ArXiv:1804.07744.
View | Files available | Download (ext.) | arXiv
 
[106]
2017 | Journal Article | IST-REx-ID: 1337   OA
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2017). Universality for general Wigner-type matrices. Probability Theory and Related Fields, 169(3–4), 667–727. https://doi.org/10.1007/s00440-016-0740-2
View | Files available | DOI
 
[105]
2017 | Journal Article | IST-REx-ID: 1010
Alt, J., Erdös, L., & Krüger, T. H. (2017). Local law for random Gram matrices. Electronic Journal of Probability, 22, 25. https://doi.org/10.1214/17-EJP42
View | Files available | DOI | arXiv
 
[104]
2017 | Journal Article | IST-REx-ID: 1528   OA
Bao, Z., & Erdös, L. (2017). Delocalization for a class of random block band matrices. Probability Theory and Related Fields, 167(3–4), 673–776. https://doi.org/10.1007/s00440-015-0692-y
View | Files available | DOI
 
[103]
2017 | Book | IST-REx-ID: 567
Erdös, L., & Yau, H. (2017). A dynamical approach to random matrix theory (Vol. 28). American Mathematical Society.
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[102]
2017 | Journal Article | IST-REx-ID: 721   OA
Ajanki, O. H., Krüger, T. H., & Erdös, L. (2017). Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics, 70(9), 1672–1705. https://doi.org/10.1002/cpa.21639
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[101]
2017 | Journal Article | IST-REx-ID: 733   OA
Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics, 319, 251–291. https://doi.org/10.1016/j.aim.2017.08.028
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[100]
2017 | Journal Article | IST-REx-ID: 1207   OA
Bao, Z., Erdös, L., & Schnelli, K. (2017). Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics, 349(3), 947–990. https://doi.org/10.1007/s00220-016-2805-6
View | Files available | DOI
 
[99]
2017 | Journal Article | IST-REx-ID: 1144
Erdös, L., & Schröder, D. J. (2017). Fluctuations of functions of Wigner matrices. Electronic Communications in Probability, 21. https://doi.org/10.1214/16-ECP38
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[98]
2017 | Journal Article | IST-REx-ID: 615   OA
Erdös, L., & Schnelli, K. (2017). Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics, 53(4), 1606–1656. https://doi.org/10.1214/16-AIHP765
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[97]
2017 | Journal Article | IST-REx-ID: 483   OA
Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics, 21(3), 739–800. https://doi.org/10.4310/ATMP.2017.v21.n3.a5
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[96]
2016 | Journal Article | IST-REx-ID: 1434   OA
Bao, Z., Erdös, L., & Schnelli, K. (2016). Local stability of the free additive convolution. Journal of Functional Analysis, 271(3), 672–719. https://doi.org/10.1016/j.jfa.2016.04.006
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[95]
2016 | Journal Article | IST-REx-ID: 1489   OA
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2016). Local spectral statistics of Gaussian matrices with correlated entries. Journal of Statistical Physics, 163(2), 280–302. https://doi.org/10.1007/s10955-016-1479-y
View | Files available | DOI
 
[94]
2016 | Journal Article | IST-REx-ID: 1280   OA
Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2016). Fixed energy universality for generalized wigner matrices. Communications on Pure and Applied Mathematics, 69(10), 1815–1881. https://doi.org/10.1002/cpa.21624
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[93]
2015 | Journal Article | IST-REx-ID: 1508   OA
Erdös, L., & Yau, H. (2015). Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society, 17(8), 1927–2036. https://doi.org/10.4171/JEMS/548
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[92]
2015 | Journal Article | IST-REx-ID: 1864   OA
Erdös, L., & Knowles, A. (2015). The Altshuler–Shklovskii formulas for random band matrices II: The general case. Annales Henri Poincare, 16(3), 709–799. https://doi.org/10.1007/s00023-014-0333-5
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[91]
2015 | Journal Article | IST-REx-ID: 2166   OA
Erdös, L., & Knowles, A. (2015). The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Communications in Mathematical Physics, 333(3), 1365–1416. https://doi.org/10.1007/s00220-014-2119-5
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[90]
2014 | Journal Article | IST-REx-ID: 2019   OA
Erdös, L., & Schröder, D. J. (2014). Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry, 17(3–4), 441–464. https://doi.org/10.1007/s11040-014-9164-3
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[89]
2014 | Journal Article | IST-REx-ID: 2179   OA
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2014). Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability, 19. https://doi.org/10.1214/ECP.v19-3121
View | Files available | DOI
 
[88]
2014 | Journal Article | IST-REx-ID: 2225   OA
Bloemendal, A., Erdös, L., Knowles, A., Yau, H., & Yin, J. (2014). Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability, 19, 33. https://doi.org/10.1214/EJP.v19-3054
View | Files available | DOI
 
[87]
2014 | Conference Paper | IST-REx-ID: 1507   OA
Erdös, L. (2014). Random matrices, log-gases and Hölder regularity (Vol. 3, pp. 214–236). Presented at the ICM: International Congress of Mathematicians, Seoul, Korea: Kyung Moon SA Co. Ltd.
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[86]
2014 | Journal Article | IST-REx-ID: 1937   OA
Bourgade, P., Erdös, L., & Yau, H. (2014). Edge universality of beta ensembles. Communications in Mathematical Physics, 332(1), 261–353. https://doi.org/10.1007/s00220-014-2120-z
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[85]
2014 | Journal Article | IST-REx-ID: 2699   OA
Erdös, L., Bourgade, P., & Yau, H. (2014). Universality of general β-ensembles. Duke Mathematical Journal, 163(6), 1127–1190. https://doi.org/10.1215/00127094-2649752
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[84]
2013 | Journal Article | IST-REx-ID: 2780   OA
Erdös, L., Knowles, A., & Yau, H. (2013). Averaging fluctuations in resolvents of random band matrices. Annales Henri Poincare, 14(8), 1837–1926. https://doi.org/10.1007/s00023-013-0235-y
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[83]
2013 | Journal Article | IST-REx-ID: 2697   OA
Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). Delocalization and diffusion profile for random band matrices. Communications in Mathematical Physics, 323(1), 367–416. https://doi.org/10.1007/s00220-013-1773-3
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[82]
2013 | Journal Article | IST-REx-ID: 2781   OA
Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). Spectral statistics of Erdős-Rényi graphs I: Local semicircle law. Annals of Probability, 41(3 B), 2279–2375. https://doi.org/10.1214/11-AOP734
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[81]
2013 | Journal Article | IST-REx-ID: 2837   OA
Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). The local semicircle law for a general class of random matrices. Electronic Journal of Probability, 18(59), 1–58. https://doi.org/10.1214/EJP.v18-2473
View | Files available | DOI
 
[80]
2013 | Journal Article | IST-REx-ID: 2698   OA
Erdös, L., Fournais, S., & Solovej, J. (2013). Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society, 15(6), 2093–2113. https://doi.org/10.4171/JEMS/416
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[79]
2013 | Journal Article | IST-REx-ID: 2782   OA
Erdös, L., & Farrell, B. (2013). Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics, 152(6), 1003–1032. https://doi.org/10.1007/s10955-013-0807-8
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[78]
2012 | Journal Article | IST-REx-ID: 2772
Erdös, L., Fournais, S., & Solovej, J. (2012). Second order semiclassics with self generated magnetic fields. Annales Henri Poincare, 13(4), 671–730. https://doi.org/10.1007/s00023-011-0150-z
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[77]
2012 | Journal Article | IST-REx-ID: 2777
Erdös, L., Fournais, S., & Solovej, J. (2012). Relativistic Scott correction in self-generated magnetic fields. Journal of Mathematical Physics, 53(9). https://doi.org/10.1063/1.3697417
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[76]
2012 | Preprint | IST-REx-ID: 2696   OA
Erdös, L. (2012). Universality for random matrices and log-gases. ArXiv. ArXiv.
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[75]
2012 | Journal Article | IST-REx-ID: 2773
Erdös, L., & Yau, H. (2012). A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability, 17. https://doi.org/10.1214/EJP.v17-1779
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[74]
2012 | Journal Article | IST-REx-ID: 2778
Bourgade, P., Erdös, L., & Yau, H. (2012). Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics, 53(9). https://doi.org/10.1063/1.4751478
View | DOI
 
[73]
2012 | Conference Paper | IST-REx-ID: 2700   OA
Erdös, L. (2012). Lecture notes on quantum Brownian motion (Vol. 95, pp. 3–98). Presented at the Les Houches Summer School 2010, Oxford University Press.
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[72]
2012 | Journal Article | IST-REx-ID: 2767
Erdös, L., Yau, H., & Yin, J. (2012). Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields, 154(1–2), 341–407. https://doi.org/10.1007/s00440-011-0390-3
View | DOI
 
[71]
2012 | Journal Article | IST-REx-ID: 2774
Erdös, L., Fournais, S., & Solovej, J. (2012). Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics, 312(3), 847–882. https://doi.org/10.1007/s00220-012-1468-1
View | DOI
 
[70]
2012 | Journal Article | IST-REx-ID: 2779
Erdös, L., & Hasler, D. (2012). Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare, 13(8), 1719–1731. https://doi.org/10.1007/s00023-012-0177-9
View | DOI
 
[69]
2012 | Journal Article | IST-REx-ID: 2768
Erdös, L., & Hasler, D. (2012). Wegner estimate and Anderson localization for random magnetic fields. Communications in Mathematical Physics, 309(2), 507–542. https://doi.org/10.1007/s00220-011-1373-z
View | DOI
 
[68]
2012 | Journal Article | IST-REx-ID: 2770
Erdös, L., Yau, H., & Yin, J. (2012). Rigidity of eigenvalues of generalized Wigner matrices. Advances in Mathematics, 229(3), 1435–1515. https://doi.org/10.1016/j.aim.2011.12.010
View | DOI
 
[67]
2012 | Journal Article | IST-REx-ID: 2775
Erdös, L., & Yau, H. (2012). Universality of local spectral statistics of random matrices. Bulletin of the American Mathematical Society, 49(3), 377–414. https://doi.org/10.1090/S0273-0979-2012-01372-1
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[66]
2012 | Journal Article | IST-REx-ID: 2769
Erdös, L., Schlein, B., Yau, H., & Yin, J. (2012). The local relaxation flow approach to universality of the local statistics for random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics, 48(1), 1–46. https://doi.org/10.1214/10-AIHP388
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[65]
2012 | Journal Article | IST-REx-ID: 2771
Erdös, L., & Hasler, D. (2012). Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics, 146(5), 900–923. https://doi.org/10.1007/s10955-012-0445-6
View | DOI
 
[64]
2012 | Journal Article | IST-REx-ID: 2776
Erdös, L., Knowles, A., Yau, H., & Yin, J. (2012). Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical Physics, 314(3), 587–640. https://doi.org/10.1007/s00220-012-1527-7
View | DOI
 
[63]
2011 | Book Review | IST-REx-ID: 2765
Erdös, L. (2011). Universality of Wigner random matrices: A survey of recent results. Russian Mathematical Surveys. IOP Publishing Ltd. https://doi.org/10.1070/RM2011v066n03ABEH004749
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[62]
2011 | Journal Article | IST-REx-ID: 2766
Erdös, L., & Knowles, A. (2011). Quantum diffusion and delocalization for band matrices with general distribution. Annales Henri Poincare, 12(7), 1227–1319. https://doi.org/10.1007/s00023-011-0104-5
View | DOI
 
[61]
2011 | Journal Article | IST-REx-ID: 2717
Erdös, L., & Knowles, A. (2011). Quantum diffusion and eigenfunction delocalization in a random band matrix model. Communications in Mathematical Physics, 303(2), 509–554. https://doi.org/10.1007/s00220-011-1204-2
View | DOI
 
[60]
2011 | Journal Article | IST-REx-ID: 2764
Erdös, L., Schlein, B., & Yau, H. (2011). Universality of random matrices and local relaxation flow. Inventiones Mathematicae, 185(1), 75–119. https://doi.org/10.1007/s00222-010-0302-7
View | DOI
 
[59]
2010 | Journal Article | IST-REx-ID: 2704
Erdös, L., Schlein, B., & Yau, H. (2010). Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate. Annals of Mathematics, 172(1), 291–370. https://doi.org/10.4007/annals.2010.172.291
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[58]
2010 | Journal Article | IST-REx-ID: 2761
Erdös, L., Ramírez, J., Schlein, B., & Yau, H. (2010). Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation. Electronic Journal of Probability, 15(18), 526–603. https://doi.org/10.1214/EJP.v15-768
View | DOI
 
[57]
2010 | Journal Article | IST-REx-ID: 2762
Erdös, L., Ramírez, J., Yau, H., Péché, S., & Schlein, B. (2010). Bulk universality for Wigner matrices. Communications on Pure and Applied Mathematics, 63(7), 895–925. https://doi.org/10.1002/cpa.20317
View | DOI
 
[56]
2010 | Journal Article | IST-REx-ID: 2701   OA
Erdös, L., Schlein, B., & Yau, H. (2010). Wegner estimate and level repulsion for Wigner random matrices. International Mathematics Research Notices, (3), 436–479. https://doi.org/10.1093/imrn/rnp136
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[55]
2010 | Journal Article | IST-REx-ID: 2756
Erdös, L., & Solovej, J. (2010). Ground state energy of large atoms in a self-generated magnetic field. Communications in Mathematical Physics, 294(1), 229–249. https://doi.org/10.1007/s00220-009-0869-2
View | DOI
 
[54]
2010 | Journal Article | IST-REx-ID: 2763
Erdös, L., Ramírez, J., Schlein, B., Tao, T., Van, V., & Yau, H. (2010). Bulk universality for Wigner Hermitian matrices with subexponential decay. Mathematical Research Letters, 17(4), 667–674.
View
 
[53]
2009 | Journal Article | IST-REx-ID: 2758
Erdös, L., Schlein, B., & Yau, H. (2009). Local semicircle law and complete delocalization for Wigner random matrices. Communications in Mathematical Physics, 287(2), 641–655. https://doi.org/10.1007/s00220-008-0636-9
View | DOI
 
[52]
2009 | Journal Article | IST-REx-ID: 2760
Erdös, L., Schlein, B., & Yau, H. (2009). Rigorous derivation of the gross-pitaevskii equation with a large interaction potential. Journal of the American Mathematical Society, 22(4), 1099–1156. https://doi.org/10.1090/S0894-0347-09-00635-3
View | DOI
 
[51]
2009 | Journal Article | IST-REx-ID: 2703
Erdös, L., Schlein, B., & Yau, H. (2009). Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices. Annals of Probability, 37(3), 815–852. https://doi.org/10.1214/08-AOP421
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[50]
2009 | Journal Article | IST-REx-ID: 2759
Erdös, L., Michelangeli, A., & Schlein, B. (2009). Dynamical formation of correlations in a Bose-Einstein condensate. Communications in Mathematical Physics, 289(3), 1171–1210. https://doi.org/10.1007/s00220-009-0828-y
View | DOI
 
[49]
2009 | Journal Article | IST-REx-ID: 2757
Erdös, L., & Schlein, B. (2009). Quantum dynamics with mean field interactions: A new approach. Journal of Statistical Physics, 134(5–6), 859–870. https://doi.org/10.1007/s10955-008-9570-7
View | DOI
 
[48]
2008 | Journal Article | IST-REx-ID: 2753
Erdös, L., Salmhofer, M., & Yau, H. (2008). Quantum diffusion of the random Schrödinger evolution in the scaling limit. Acta Mathematica, 200(2), 211–277. https://doi.org/10.1007/s11511-008-0027-2
View | DOI
 
[47]
2008 | Journal Article | IST-REx-ID: 2754
Adami, R., & Erdös, L. (2008). Rate of decoherence for an electron weakly coupled to a phonon gas. Journal of Statistical Physics, 132(2), 301–328. https://doi.org/10.1007/s10955-008-9561-8
View | DOI
 
[46]
2008 | Journal Article | IST-REx-ID: 2755
Erdös, L., Schlein, B., & Yau, H. (2008). Ground-state energy of a low-density Bose gas: A second-order upper bound. Physical Review A - Atomic, Molecular, and Optical Physics, 78(5). https://doi.org/10.1103/PhysRevA.78.053627
View | DOI
 
[45]
2008 | Conference Paper | IST-REx-ID: 2702   OA
Erdös, L., Salmhofer, M., & Yau, H. (2008). Feynman graphs and renormalization in quantum diffusion (pp. 167–182). Presented at the Symposium in Honor of Wolfhart Zimmermann’s 80th Birthday, World Scientific Publishing. https://doi.org/10.1142/9789812833556_0011
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[44]
2007 | Book Chapter | IST-REx-ID: 2705   OA
Erdös, L. (2007). Recent developments in quantum mechanics with magnetic fields. In F. Gesztesy, P. Deift, P. Galvez, P. Perry, & W. Schlag (Eds.), Spectral Theory and Mathematical Physics: a Festschrift in Honor of Barry Simon’s 60th Birthday (Vol. 76, pp. 401–428). American Mathematical Society.
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[43]
2007 | Journal Article | IST-REx-ID: 2748
Erdös, L., Schlein, B., & Yau, H. (2007). Rigorous derivation of the Gross-Pitaevskii equation. Physical Review Letters, 98(4). https://doi.org/10.1103/PhysRevLett.98.040404
View | DOI
 
[42]
2007 | Journal Article | IST-REx-ID: 2750
Erdös, L., Salmhofer, M., & Yau, H. (2007). Quantum diffusion of the random Schrödinger evolution in the scaling limit II. The recollision diagrams. Communications in Mathematical Physics, 271(1), 1–53. https://doi.org/10.1007/s00220-006-0158-2
View | DOI
 
[41]
2007 | Book Review | IST-REx-ID: 2749
Erdös, L., Schlein, B., & Yau, H. (2007). Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-006-0022-1
View | DOI
 
[40]
2007 | Journal Article | IST-REx-ID: 2751
Erdös, L., Salmhofer, M., & Yau, H. (2007). Quantum diffusion for the Anderson model in the scaling limit. Annales Henri Poincare, 8(4), 621–685. https://doi.org/10.1007/s00023-006-0318-0
View | DOI
 
[39]
2007 | Journal Article | IST-REx-ID: 2752
Erdös, L., & Salmhofer, M. (2007). Decay of the Fourier transform of surfaces with vanishing curvature. Mathematische Zeitschrift, 257(2), 261–294. https://doi.org/10.1007/s00209-007-0125-4
View | DOI
 
[38]
2006 | Conference Paper | IST-REx-ID: 2746
Erdös, L., Salmhofer, M., & Yau, H. (2006). Towards the quantum Brownian motion (Vol. 690, pp. 233–257). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. https://doi.org/10.1007/3-540-34273-7_18
View | DOI
 
[37]
2006 | Journal Article | IST-REx-ID: 2747
Erdös, L., Schlein, B., & Yau, H. (2006). Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate. Communications on Pure and Applied Mathematics, 59(12), 1659–1741. https://doi.org/10.1002/cpa.20123
View | DOI
 
[36]
2006 | Journal Article | IST-REx-ID: 2745
Elgart, A., Erdös, L., Schlein, B., & Yau, H. (2006). Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons. Archive for Rational Mechanics and Analysis, 179(2), 265–283. https://doi.org/10.1007/s00205-005-0388-z
View | DOI
 
[35]
2005 | Journal Article | IST-REx-ID: 2743
Erdös, L., Hasler, D., & Solovej, J. (2005). Existence of the D0-D4 bound state: A detailed proof. Annales Henri Poincare, 6(2), 247–267. https://doi.org/10.1007/s00023-005-0205-0
View | DOI
 
[34]
2005 | Journal Article | IST-REx-ID: 2744
Eng, D., & Erdös, L. (2005). The linear Boltzmann equation as the low density limit of a random Schrödinger equation. Reviews in Mathematical Physics, 17(6), 669–743. https://doi.org/10.1142/S0129055X0500242X
View | DOI
 
[33]
2004 | Journal Article | IST-REx-ID: 2741
Erdös, L., & Solovej, J. (2004). Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field. Annales Henri Poincare, 5(4), 671–741. https://doi.org/10.1007/s00023-004-0180-x
View | DOI
 
[32]
2004 | Journal Article | IST-REx-ID: 2742
Elgart, A., Erdös, L., Schlein, B., & Yau, H. (2004). Nonlinear Hartree equation as the mean field limit of weakly coupled fermions. Journal de Mathématiques Pures et Appliquées, 83(10), 1241–1273. https://doi.org/10.1016/j.matpur.2004.03.006
View | DOI
 
[31]
2004 | Journal Article | IST-REx-ID: 2706
Erdös, L., & Solovej, J. (2004). Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength. Journal of Statistical Physics, 116(1–4), 475–506. https://doi.org/10.1023/B:JOSS.0000037216.45270.1d
View | DOI
 
[30]
2004 | Journal Article | IST-REx-ID: 2707
Erdös, L., Salmhofer, M., & Yau, H. (2004). On the quantum Boltzmann equation. Journal of Statistical Physics, 116(1–4), 367–380. https://doi.org/10.1023/B:JOSS.0000037224.56191.ed
View | DOI
 
[29]
2002 | Journal Article | IST-REx-ID: 2739
Erdös, L., & Vougalter, V. (2002). Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields. Communications in Mathematical Physics, 225(2), 399–421. https://doi.org/10.1007/s002200100585
View | DOI
 
[28]
2002 | Conference Paper | IST-REx-ID: 2708
Erdös, L. (2002). Two dimensional Pauli operator via scalar potential (Vol. 307, pp. 129–133). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. https://doi.org/10.1090/conm/307
View | DOI
 
[27]
2002 | Journal Article | IST-REx-ID: 2737
Bardos, C., Erdös, L., Golse, F., Mauser, N., & Yau, H. (2002). Derivation of the Schrödinger-Poisson equation from the quantum N-body problem. Comptes Rendus Mathematique, 334(6), 515–520. https://doi.org/10.1016/S1631-073X(02)02253-7
View | DOI
 
[26]
2002 | Conference Paper | IST-REx-ID: 2694
Erdös, L. (2002). Scaling limits of Schrödinger quantum mechanics (Vol. 597, pp. 487–506). Presented at the 38th Winter School of Theoretical Physics : Dynamical Semigroups: Dissipation, Chaos, Quanta, Springer. https://doi.org/10.1007/3-540-46122-1_19
View | DOI
 
[25]
2002 | Journal Article | IST-REx-ID: 2738
Erdös, L. (2002). Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics, 107(5–6), 1043–1127. https://doi.org/10.1023/A:1015157624384
View | DOI
 
[24]
2002 | Journal Article | IST-REx-ID: 2740
Erdös, L. (2002). Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions. Annales de l’Institut Fourier, 52(6), 1833–1874+XI+VII. https://doi.org/10.5802/aif.1936
View | DOI
 
[23]
2001 | Journal Article | IST-REx-ID: 2734
Erdös, L., & Solovej, J. (2001). The kernel of Dirac operators on S3 and R3. Reviews in Mathematical Physics, 13(10), 1247–1280. https://doi.org/10.1142/S0129055X01000983
View | DOI
 
[22]
2001 | Journal Article | IST-REx-ID: 2709
Erdös, L. (2001). Long time dynamics of an electron in a weakly coupled phonon field. ICMP: International Congress on Mathematical Physics, 273–281.
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[21]
2001 | Journal Article | IST-REx-ID: 2735
Erdös, L. (2001). Lifschitz tail in a magnetic field: Coexistence of classical and quantum behavior in the borderline case. Probability Theory and Related Fields, 121(2), 219–236. https://doi.org/10.1007/PL00008803
View | DOI
 
[20]
2001 | Journal Article | IST-REx-ID: 2736   OA
Erdös, L., & Yau, H. (2001). Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Advances in Theoretical and Mathematical Physics, 5(6), 1169–1205.
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[19]
2000 | Conference Paper | IST-REx-ID: 2710
Erdös, L. (2000). The kernel of Dirac operators on S3 and R3 (Vol. 16, pp. 111–119). Presented at the Differential Equations and Mathematical Physics, American Mathematical Society.
View
 
[18]
2000 | Journal Article | IST-REx-ID: 2731
Erdös, L., & Yau, H. (2000). Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation. Communications on Pure and Applied Mathematics, 53(6), 667–735. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5
View | DOI
 
[17]
2000 | Journal Article | IST-REx-ID: 2732
Castella, F., Erdös, L., Frommlet, F., & Markowich, P. (2000). Fokker-Planck equations as scaling limits of reversible quantum systems. Journal of Statistical Physics, 100(3–4), 543–601. https://doi.org/10.1023/A:1018667323830
View | DOI
 
[16]
2000 | Journal Article | IST-REx-ID: 2733
Erdös, L., Loss, M., & Vougalter, V. (2000). Diamagnetic behavior of sums Dirichlet eigenvalues. Annales de l’Institut Fourier, 50(3), 891–907. https://doi.org/10.5802/aif.1777
View | DOI
 
[15]
1999 | Conference Paper | IST-REx-ID: 2711
Erdös, L. (1999). Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation (Vol. 108, pp. 233–242). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. https://doi.org/10.1007/978-3-0348-8745-8_20
View | DOI
 
[14]
1999 | Journal Article | IST-REx-ID: 2730
Erdös, L., & Solovej, J. (1999). Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. Duke Mathematical Journal, 96(1), 127–173. https://doi.org/10.1215/S0012-7094-99-09604-7
View | DOI
 
[13]
1998 | Conference Paper | IST-REx-ID: 2695
Erdös, L., & Yau, H. (1998). Linear Boltzmann equation as scaling limit of quantum Lorentz gas (Vol. 217, pp. 137–155). Presented at the Differential Equations and Mathematical Physics, American Mathematical Society. https://doi.org/10.1090/conm/217
View | DOI
 
[12]
1998 | Journal Article | IST-REx-ID: 2728
Erdös, L. (1998). Lifschitz tail in a magnetic field: The nonclassical regime. Probability Theory and Related Fields, 112(3), 321–371. https://doi.org/10.1007/s004400050193
View | DOI
 
[11]
1997 | Journal Article | IST-REx-ID: 2727
Erdös, L. (1997). Dia- and paramagnetism for nonhomogeneous magnetic fields. Journal of Mathematical Physics, 38(3), 1289–1317. https://doi.org/10.1063/1.531909
View | DOI
 
[10]
1997 | Journal Article | IST-REx-ID: 2729
Erdös, L., & Solovej, J. (1997). Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates. Communications in Mathematical Physics, 188(3), 599–656. https://doi.org/10.1007/s002200050181
View | DOI
 
[9]
1996 | Journal Article | IST-REx-ID: 2725
Erdös, L. (1996). Rayleigh-type isoperimetric inequality with a homogeneous magnetic field. Calculus of Variations and Partial Differential Equations, 4(3), 283–292. https://doi.org/10.1007/BF01254348
View | DOI
 
[8]
1996 | Journal Article | IST-REx-ID: 2726
Erdös, L. (1996). Gaussian decay of the magnetic eigenfunctions. Geometric and Functional Analysis, 6(2), 231–248. https://doi.org/10.1007/BF02247886
View | DOI
 
[7]
1995 | Conference Paper | IST-REx-ID: 2712
Erdös, L. (1995). Magnetic Lieb-Thirring inequalities and stochastic oscillatory integrals (Vol. 78, pp. 127–132). Presented at the Partial Differential Operators and Mathematical Physics, Birkhäuser. https://doi.org/10.1007/978-3-0348-9092-2_13
View | DOI
 
[6]
1995 | Journal Article | IST-REx-ID: 2724
Erdös, L. (1995). Magnetic Lieb-Thirring inequalities. Communications in Mathematical Physics, 170(3), 629–668. https://doi.org/10.1007/BF02099152
View | DOI
 
[5]
1994 | Journal Article | IST-REx-ID: 2713
Erdös, L. (1994). Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator. Duke Mathematical Journal, 76(2), 541–566. https://doi.org/10.1215/S0012-7094-94-07619-9
View | DOI
 
[4]
1993 | Journal Article | IST-REx-ID: 2723
Erdös, L. (1993). Ground-state density of the Pauli operator in the large field limit. Letters in Mathematical Physics, 29(3), 219–240. https://doi.org/10.1007/BF00761110
View | DOI
 
[3]
1992 | Journal Article | IST-REx-ID: 2722
Erdös, L., & Tuyen, D. (1992). Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers. Communications in Mathematical Physics, 143(3), 451–466. https://doi.org/10.1007/BF02099260
View | DOI
 
[2]
1992 | Journal Article | IST-REx-ID: 2714
Erdös, L. (1992). On some problems of P. Turán concerning power sums of complex numbers. Acta Mathematica Hungarica, 59(1–2), 11–24. https://doi.org/10.1007/BF00052086
View | DOI
 
[1]
1990 | Journal Article | IST-REx-ID: 2721
Erdös, L., & Tuyen, D. (1990). Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier. Journal of Statistical Physics, 59(5–6), 1589–1602. https://doi.org/10.1007/BF01334766
View | DOI
 

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