Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.

Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.

Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 76(5), 946–1034.

Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.

Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.

Cipolloni G, Erdös L, Schröder DJ. 2023. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields.

Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13.

Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489.

Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.

Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 190(7), 128.

Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74.

Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.

Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3), 1469–1487.

Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.

Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.

Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.

Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.

Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.

Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.

Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 26, 24.

Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.

Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.

Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.

Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.

Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.

Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507.

Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348.

Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.

Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006.

Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.

Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.

Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.

Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 1(1), 101–146.

Erdös L, Götze F, Guionnet A. 2020. Random matrices. Oberwolfach Reports. 16(4), 3459–3527.

Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 173(1–2), 293–373.

Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale. Annals of Probability. 47(3), 1270–1334.

Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.

Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.

Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696.

Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals Applied Probability . 28(1), 148–203.

Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3), 3271–3290.

Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.

Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298.

Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and  cusps. arXiv, 1804.07752.

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.

Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 226p.

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.

Ajanki OH, Krüger TH, 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.

Erdös L, Schröder DJ. 2017. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 21, 86.

Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 167(3–4), 673–776.

Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 169(3–4), 667–727.

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.

Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic Journal of Probability. 22, 25.

Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 319, 251–291.

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.

Bao Z, Erdös L, Schnelli K. 2016. Local stability of the free additive convolution. Journal of Functional Analysis. 271(3), 672–719.

Ajanki OH, Erdös L, Krüger TH. 2016. Local spectral statistics of Gaussian matrices with correlated entries. Journal of Statistical Physics. 163(2), 280–302.

Erdös L, Yau H. 2015. Gap universality of generalized Wigner and ;2 ensembles. Journal of the European Mathematical Society. 17(8), 1927–2036.

Erdös L, Knowles A. 2015. The Altshuler–Shklovskii formulas for random band matrices II: The general case. Annales Henri Poincare. 16(3), 709–799.

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.

Bourgade P, Erdös L, Yau H. 2014. Edge universality of beta ensembles. Communications in Mathematical Physics. 332(1), 261–353.

Erdös L, Schröder DJ. 2014. Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. 17(3–4), 441–464.

Ajanki OH, Erdös L, Krüger TH. 2014. Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability. 19.

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.

Erdös L, Bourgade P, Yau H. 2014. Universality of general ;2-ensembles. Duke Mathematical Journal. 163(6), 1127–1190.

Erdös L. 2014. Random matrices, log-gases and Hölder regularity. Proceedings of the International Congress of Mathematicians. ICM: International Congress of Mathematicians vol. 3, 214–236.

Erdös L, Fournais S, Solovej J. 2013. Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. 15(6), 2093–2113.

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.

Erdös L, Farrell B. 2013. Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. 152(6), 1003–1032.

Erdös L, Knowles A, Yau H, Yin J. 2013. Spectral statistics of Erds-Rényi graphs I: Local semicircle law. Annals of Probability. 41(3 B), 2279–2375.

Erdös L, Knowles A, Yau H. 2013. Averaging fluctuations in resolvents of random band matrices. Annales Henri Poincare. 14(8), 1837–1926.

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.

Erdös L. 2012. Universality for random matrices and log-gases. ArXiv, .

Erdös L. 2012. Lecture notes on quantum Brownian motion. Les Houches Summer School 2010, Quantum Theory from Small to Large Scales, vol. 95, 3–98.

Erdös L, Yau H, Yin J. 2012. Rigidity of eigenvalues of generalized Wigner matrices. Advances in Mathematics. 229(3), 1435–1515.

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.

Erdös L, Yau H, Yin J. 2012. Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields. 154(1–2), 341–407.

Erdös L, Hasler D. 2012. Wegner estimate and Anderson localization for random magnetic fields. Communications in Mathematical Physics. 309(2), 507–542.

Erdös L, Yau H. 2012. Universality of local spectral statistics of random matrices. Bulletin of the American Mathematical Society. 49(3), 377–414.

Erdös L, Fournais S, Solovej J. 2012. Relativistic Scott correction in self-generated magnetic fields. Journal of Mathematical Physics. 53(9).

Erdös L, Fournais S, Solovej J. 2012. Second order semiclassics with self generated magnetic fields. Annales Henri Poincare. 13(4), 671–730.

Erdös L, Knowles A, Yau H, Yin J. 2012. Spectral statistics of Erds-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical Physics. 314(3), 587–640.

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.

Erdös L, Yau H. 2012. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 17.

Erdös L, Hasler D. 2012. Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. 146(5), 900–923.

Bourgade P, Erdös L, Yau H. 2012. Bulk universality of general ;2-ensembles with non-convex potential. Journal of Mathematical Physics. 53(9).

Erdös L, Hasler D. 2012. Wegner estimate for random magnetic Laplacian on  2. Annales Henri Poincare. 13(8), 1719–1731.

Erdös L, Knowles A. 2011. Quantum diffusion and eigenfunction delocalization in a random band matrix model. Communications in Mathematical Physics. 303(2), 509–554.

Erdös L. 2011. Universality of Wigner random matrices: A survey of recent results. Russian Mathematical Surveys. 66(3), 507–626.

Erdös L, Knowles A. 2011. Quantum diffusion and delocalization for band matrices with general distribution. Annales Henri Poincare. 12(7), 1227–1319.

Erdös L, Schlein B, Yau H. 2011. Universality of random matrices and local relaxation flow. Inventiones Mathematicae. 185(1), 75–119.

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.

Erdös L, Schlein B, Yau H. 2010. Wegner estimate and level repulsion for Wigner random matrices. International Mathematics Research Notices. (3), 436–479.

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.

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.

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.

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.

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.

Erdös L, Michelangeli A, Schlein B. 2009. Dynamical formation of correlations in a Bose-Einstein condensate. Communications in Mathematical Physics. 289(3), 1171–1210.

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.