L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” Annals of Applied Probability, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” Probability Theory and Related Fields, vol. 185. Springer Nature, pp. 1183–1218, 2023.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” Communications on Pure and Applied Mathematics, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.

L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue of Wigner matrices,” Bernoulli, vol. 29, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1063–1079, 2023.

G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” Communications in Mathematical Physics, vol. 401. Springer Nature, pp. 1665–1700, 2023.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2023.

G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” Electronic Communications in Probability, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems for Wigner matrices,” Annals of Applied Probability, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 447–489, 2023.

L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.

S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation hypothesis for translation invariant spin systems,” Journal of Statistical Physics, vol. 190, no. 7. Springer Nature, 2023.

G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 11. Cambridge University Press, 2023.

G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” The Annals of Probability, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.

G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the shifted real Ginibre ensemble,” SIAM Journal on Matrix Analysis and Applications, vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487, 2022.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” Journal of Functional Analysis, vol. 282, no. 8. Elsevier, 2022.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” Annals of Probability, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.

G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no. 10. AIP Publishing, 2022.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” Electronic Journal of Probability, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.

Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.

L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature, pp. 4205–4269, 2021.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” Communications in Mathematical Physics, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021.

J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” Probability and Mathematical Physics, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2021.

L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” Journal of Functional Analysis, vol. 278, no. 12. Elsevier, 2020.

Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” Journal d’Analyse Mathematique, vol. 142. Springer Nature, pp. 323–348, 2020.

Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” Journal of Functional Analysis, vol. 279, no. 7. Elsevier, 2020.

G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020.

L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” Communications in Mathematical Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.

J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” Documenta Mathematica, vol. 25. EMS Press, pp. 1421–1539, 2020.

J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” Annals of Probability, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.

G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” Probability and Mathematical Physics, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.

L. Erdös, F. Götze, and A. Guionnet, “Random matrices,” Oberwolfach Reports, vol. 16, no. 4. European Mathematical Society, pp. 3459–3527, 2020.

O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.

Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.

L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019.

G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.

J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” Annales de l’institut Henri Poincare, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.

J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics, pp. 148–203, 2018.

L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018.

L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.

L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.

J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and  cusps,” arXiv. .

P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 739–800, 2017.

L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory, vol. 28. American Mathematical Society, 2017.

L. Erdös and K. Schnelli, “Universality for random matrix flows with time dependent density,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656, 2017.

O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic vector equations on the complex upper half plane,” Communications on Pure and Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017.

L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21. Institute of Mathematical Statistics, 2017.

Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,” Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp. 673–776, 2017.

O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type matrices,” Probability Theory and Related Fields, vol. 169, no. 3–4. Springer, pp. 667–727, 2017.

Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” Communications in Mathematical Physics, vol. 349, no. 3. Springer, pp. 947–990, 2017.

J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017.

Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” Advances in Mathematics, vol. 319. Academic Press, pp. 251–291, 2017.

P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Fixed energy universality for generalized wigner matrices,” Communications on Pure and Applied Mathematics, vol. 69, no. 10. Wiley-Blackwell, pp. 1815–1881, 2016.

Z. Bao, L. Erdös, and K. Schnelli, “Local stability of the free additive convolution,” Journal of Functional Analysis, vol. 271, no. 3. Academic Press, pp. 672–719, 2016.

O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local spectral statistics of Gaussian matrices with correlated entries,” Journal of Statistical Physics, vol. 163, no. 2. Springer, pp. 280–302, 2016.

L. Erdös and H. Yau, “Gap universality of generalized Wigner and ;2 ensembles,” Journal of the European Mathematical Society, vol. 17, no. 8. European Mathematical Society, pp. 1927–2036, 2015.

L. Erdös and A. Knowles, “The Altshuler–Shklovskii formulas for random band matrices II: The general case,” Annales Henri Poincare, vol. 16, no. 3. Springer, pp. 709–799, 2015.

L. Erdös and A. Knowles, “The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case,” Communications in Mathematical Physics, vol. 333, no. 3. Springer, pp. 1365–1416, 2015.

P. Bourgade, L. Erdös, and H. Yau, “Edge universality of beta ensembles,” Communications in Mathematical Physics, vol. 332, no. 1. Springer, pp. 261–353, 2014.

L. Erdös and D. J. Schröder, “Phase transition in the density of states of quantum spin glasses,” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4. Springer, pp. 441–464, 2014.

O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local semicircle law with imprimitive variance matrix,” Electronic Communications in Probability, vol. 19. Institute of Mathematical Statistics, 2014.

A. Bloemendal, L. Erdös, A. Knowles, H. Yau, and J. Yin, “Isotropic local laws for sample covariance and generalized Wigner matrices,” Electronic Journal of Probability, vol. 19. Institute of Mathematical Statistics, 2014.

L. Erdös, P. Bourgade, and H. Yau, “Universality of general ;2-ensembles,” Duke Mathematical Journal, vol. 163, no. 6. Duke University Press, pp. 1127–1190, 2014.

L. Erdös, “Random matrices, log-gases and Hölder regularity,” in Proceedings of the International Congress of Mathematicians, Seoul, Korea, 2014, vol. 3, pp. 214–236.

L. Erdös, S. Fournais, and J. Solovej, “Stability and semiclassics in self-generated fields,” Journal of the European Mathematical Society, vol. 15, no. 6. European Mathematical Society, pp. 2093–2113, 2013.

L. Erdös, A. Knowles, H. Yau, and J. Yin, “Delocalization and diffusion profile for random band matrices,” Communications in Mathematical Physics, vol. 323, no. 1. Springer, pp. 367–416, 2013.

L. Erdös and B. Farrell, “Local eigenvalue density for general MANOVA matrices,” Journal of Statistical Physics, vol. 152, no. 6. Springer, pp. 1003–1032, 2013.

L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erds-Rényi graphs I: Local semicircle law,” Annals of Probability, vol. 41, no. 3 B. Institute of Mathematical Statistics, pp. 2279–2375, 2013.

L. Erdös, A. Knowles, and H. Yau, “Averaging fluctuations in resolvents of random band matrices,” Annales Henri Poincare, vol. 14, no. 8. Birkhäuser, pp. 1837–1926, 2013.

L. Erdös, A. Knowles, H. Yau, and J. Yin, “The local semicircle law for a general class of random matrices,” Electronic Journal of Probability, vol. 18, no. 59. Institute of Mathematical Statistics, pp. 1–58, 2013.

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

L. Erdös, “Lecture notes on quantum Brownian motion,” presented at the Les Houches Summer School 2010, 2012, vol. 95, pp. 3–98.

L. Erdös, H. Yau, and J. Yin, “Rigidity of eigenvalues of generalized Wigner matrices,” Advances in Mathematics, vol. 229, no. 3. Academic Press, pp. 1435–1515, 2012.

L. Erdös, B. Schlein, H. Yau, and J. Yin, “The local relaxation flow approach to universality of the local statistics for random matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 48, no. 1. Institute of Mathematical Statistics, pp. 1–46, 2012.

L. Erdös, H. Yau, and J. Yin, “Bulk universality for generalized Wigner matrices,” Probability Theory and Related Fields, vol. 154, no. 1–2. Springer, pp. 341–407, 2012.

L. Erdös and D. Hasler, “Wegner estimate and Anderson localization for random magnetic fields,” Communications in Mathematical Physics, vol. 309, no. 2. Springer, pp. 507–542, 2012.

L. Erdös and H. Yau, “Universality of local spectral statistics of random matrices,” Bulletin of the American Mathematical Society, vol. 49, no. 3. American Mathematical Society, pp. 377–414, 2012.

L. Erdös, S. Fournais, and J. Solovej, “Relativistic Scott correction in self-generated magnetic fields,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012.

L. Erdös, S. Fournais, and J. Solovej, “Second order semiclassics with self generated magnetic fields,” Annales Henri Poincare, vol. 13, no. 4. Birkhäuser, pp. 671–730, 2012.

L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erds-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues,” Communications in Mathematical Physics, vol. 314, no. 3. Springer, pp. 587–640, 2012.

L. Erdös, S. Fournais, and J. Solovej, “Scott correction for large atoms and molecules in a self-generated magnetic field,” Communications in Mathematical Physics, vol. 312, no. 3. Springer, pp. 847–882, 2012.

L. Erdös and H. Yau, “A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices,” Electronic Journal of Probability, vol. 17. Institute of Mathematical Statistics, 2012.

L. Erdös and D. Hasler, “Anderson localization at band edges for random magnetic fields,” Journal of Statistical Physics, vol. 146, no. 5. Springer, pp. 900–923, 2012.

P. Bourgade, L. Erdös, and H. Yau, “Bulk universality of general ;2-ensembles with non-convex potential,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012.

L. Erdös and D. Hasler, “Wegner estimate for random magnetic Laplacian on  2,” Annales Henri Poincare, vol. 13, no. 8. Birkhäuser, pp. 1719–1731, 2012.

L. Erdös and A. Knowles, “Quantum diffusion and eigenfunction delocalization in a random band matrix model,” Communications in Mathematical Physics, vol. 303, no. 2. Springer, pp. 509–554, 2011.

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.

L. Erdös and A. Knowles, “Quantum diffusion and delocalization for band matrices with general distribution,” Annales Henri Poincare, vol. 12, no. 7. Birkhäuser, pp. 1227–1319, 2011.

L. Erdös, B. Schlein, and H. Yau, “Universality of random matrices and local relaxation flow,” Inventiones Mathematicae, vol. 185, no. 1. Springer, pp. 75–119, 2011.

L. Erdös, B. Schlein, and H. Yau, “Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate,” Annals of Mathematics, vol. 172, no. 1. Princeton University Press, pp. 291–370, 2010.

L. Erdös, B. Schlein, and H. Yau, “Wegner estimate and level repulsion for Wigner random matrices,” International Mathematics Research Notices, no. 3. Oxford University Press, pp. 436–479, 2010.

L. Erdös, J. Ramírez, H. Yau, S. Péché, and B. Schlein, “Bulk universality for Wigner matrices,” Communications on Pure and Applied Mathematics, vol. 63, no. 7. Wiley-Blackwell, pp. 895–925, 2010.

L. Erdös, J. Ramírez, B. Schlein, and H. Yau, “Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation,” Electronic Journal of Probability, vol. 15, no. 18. Institute of Mathematical Statistics, pp. 526–603, 2010.

L. Erdös and J. Solovej, “Ground state energy of large atoms in a self-generated magnetic field,” Communications in Mathematical Physics, vol. 294, no. 1. Springer, pp. 229–249, 2010.

L. Erdös, J. Ramírez, B. Schlein, T. Tao, V. Van, and H. Yau, “Bulk universality for Wigner Hermitian matrices with subexponential decay,” Mathematical Research Letters, vol. 17, no. 4. International Press, pp. 667–674, 2010.

L. Erdös, B. Schlein, and H. Yau, “Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices,” Annals of Probability, vol. 37, no. 3. Institute of Mathematical Statistics, pp. 815–852, 2009.

L. Erdös, A. Michelangeli, and B. Schlein, “Dynamical formation of correlations in a Bose-Einstein condensate,” Communications in Mathematical Physics, vol. 289, no. 3. Springer, pp. 1171–1210, 2009.

L. Erdös, B. Schlein, and H. Yau, “Local semicircle law and complete delocalization for Wigner random matrices,” Communications in Mathematical Physics, vol. 287, no. 2. Springer, pp. 641–655, 2009.