Universality of Wigner random matrices: a survey of recent results

L Erdős - Russian Mathematical Surveys, 2011‏ - iopscience.iop.org
This is a study of the universality of spectral statistics for large random matrices. Considered
are symmetric, Hermitian, or quaternion self-dual random matrices with independent …

[ספר][B] A dynamical approach to random matrix theory

L Erdős, HT Yau - 2017‏ - books.google.com
A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York
University This book is a concise and self-contained introduction of recent techniques to …

[ספר][B] Eigenvalue distribution of large random matrices

LA Pastur, M Shcherbina - 2011‏ - books.google.com
Random matrix theory is a wide and growing field with a variety of concepts, results, and
techniques and a vast range of applications in mathematics and the related sciences. The …

[ספר][B] Random operators

M Aizenman, S Warzel - 2015‏ - books.google.com
This book provides an introduction to the mathematical theory of disorder effects on quantum
spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics …

Universality of extremal eigenvalues of large random matrices

G Cipolloni, L Erdős, Y Xu - arxiv preprint arxiv:2312.08325, 2023‏ - arxiv.org
We prove that the spectral radius of a large random matrix $ X $ with independent,
identically distributed complex entries follows the Gumbel law irrespective of the distribution …

[HTML][HTML] Eigenvectors of random matrices: a survey

S O'Rourke, V Vu, K Wang - Journal of Combinatorial Theory, Series A, 2016‏ - Elsevier
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Random band matrices in the delocalized phase, I: Quantum unique ergodicity and universality

P Bourgade, HT Yau, J Yin - arxiv preprint arxiv:1807.01559, 2018‏ - arxiv.org
Consider $ N\times N $ symmetric one-dimensional random band matrices with general
distribution of the entries and band width $ W\geq N^{3/4+\varepsilon} $ for any …

Universality of local spectral statistics of random matrices

L Erdős, HT Yau - Bulletin of the American Mathematical Society, 2012‏ - ams.org
The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of
large random matrices exhibit universal behavior depending only on the symmetry class of …

Delocalization and diffusion profile for random band matrices

L Erdős, A Knowles, HT Yau, J Yin - Communications in Mathematical …, 2013‏ - Springer
We consider Hermitian and symmetric random band matrices H=(h xy) in d\,\geqslant\, 1 d⩾
1 dimensions. The matrix entries h xy, indexed by x, y ∈ (Z/LZ)^ dx, y∈(Z/LZ) d, are …

Entanglement transition and heterogeneity in long-range quadratic Lindbladians

ACC de Albornoz, DC Rose, A Pal - Physical Review B, 2024‏ - APS
The generation of entanglement in mixed states is relevant to quantum systems coupled to
an environment. The dissipative and mixing properties of the environment are unavoidable …