[BOOK][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 …
spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics …
Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
We study the spectral properties of the adjacency matrix in the giant connected component
of Erdös-Rényi random graphs, with average degree p and randomly distributed hop** …
of Erdös-Rényi random graphs, with average degree p and randomly distributed hop** …
Eigenvalue statistics for CMV matrices: from Poisson to clock via random matrix ensembles
R Killip, M Stoiciu - 2009 - projecteuclid.org
We study CMV matrices (discrete one-dimensional Dirac-type operators) with random
decaying coefficients. Under mild assumptions, we identify the local eigenvalue statistics in …
decaying coefficients. Under mild assumptions, we identify the local eigenvalue statistics in …
Robust nonergodicity of the ground states in the ensemble
In various chaotic quantum many-body systems, the ground states show nontrivial athermal
behavior despite the bulk states exhibiting thermalization. Such athermal states play a …
behavior despite the bulk states exhibiting thermalization. Such athermal states play a …
Operator limits of random matrices
B Virág - arxiv preprint arxiv:1804.06953, 2018 - arxiv.org
arxiv:1804.06953v1 [math.PR] 19 Apr 2018 Operator limits of random matrices Page 1 arxiv:1804.06953v1
[math.PR] 19 Apr 2018 Operator limits of random matrices Bálint Virág∗ May 25, 2014 …
[math.PR] 19 Apr 2018 Operator limits of random matrices Bálint Virág∗ May 25, 2014 …
A matrix model of a non-Hermitian -ensemble
F Mezzadri, H Taylor - arxiv preprint arxiv:2305.13184, 2023 - arxiv.org
We introduce the first random matrix model of a complex $\beta $-ensemble. The matrices
are tridiagonal and can be thought of as the non-Hermitian analogue of the Hermite $\beta …
are tridiagonal and can be thought of as the non-Hermitian analogue of the Hermite $\beta …
Level statistics of one-dimensional Schrödinger operators with random decaying potential
S Kotani, F Nakano - Festschrift Masatoshi Fukushima: In Honor of …, 2015 - World Scientific
We study the level statistics of one-dimensional Schrödinger operator with random potential
decaying like x-α at infinity. We consider the point process ξL consisting of the rescaled …
decaying like x-α at infinity. We consider the point process ξL consisting of the rescaled …
Fluctuations of interlacing sequences
S Sodin - arxiv preprint arxiv:1610.02690, 2016 - arxiv.org
In a series of works published in the 1990-s, Kerov put forth various applications of the circle
of ideas centred at the Markov moment problem to the limiting shape of random continual …
of ideas centred at the Markov moment problem to the limiting shape of random continual …
Emergent multifractality in power-law decaying eigenstates
Eigenstate multifractality is of significant interest with potential applications in various fields
of quantum physics. Most of the previous studies concentrated on fine-tuned quantum …
of quantum physics. Most of the previous studies concentrated on fine-tuned quantum …
Anderson transition at two-dimensional growth rate on antitrees and spectral theory for operators with one propagating channel
C Sadel - Annales Henri Poincaré, 2016 - Springer
We show that the Anderson model has a transition from localization to delocalization at
exactly two-dimensional growth rate on antitrees with normalized edge weights which are …
exactly two-dimensional growth rate on antitrees with normalized edge weights which are …