Fetching the paper…
Reading the bibliography…
We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension.
“Fermionic eigenvector moment flow”
Lucas Benigni · 1908
Earlier work this paper cites.
“Central Limit Theorem for Linear Eigenvalue Statistics of non-Hermitian Random Matrices”
Giorgio Cipolloni, L\’aszl\’o Erdos and Dominik Schr\"oder · 1912
Earlier work this paper cites.
“Averaging fluctuations in resolvents of random band matrices”
L\’aszl\’o Erdos, Antti Knowles and Horng-Tzer Yau · 1926
Earlier work this paper cites.
“Characteristic vectors of bordered matrices with infinite dimensions”
Eugene. Wigner · 1955
Earlier work this paper cites.
“Local semicircle law for random regular graphs”
Roland Bauerschmidt, Antti Knowles and Horng-Tzer Yau · 1960
Earlier work this paper cites.
“On chromatic number of graphs and set-systems”
P. Erdos and A. Hajnal · 1966
Earlier work this paper cites.
“ k k -degenerate graphs”
Don. Lick and Arthur. White · 1970
Earlier work this paper cites.
“Ergodic properties of eigenfunctions”
A.. Snirel’man · 1974
Earlier work this paper cites.
“Ergodicité et fonctions propres du laplacien”
Y. Colin\‘ere · 1985
Earlier work this paper cites.
“Distribution of matrix elements of chaotic systems”
M. Feingold and A. Peres · 1986
Earlier work this paper cites.
“Uniform distribution of eigenfunctions on compact hyperbolic surfaces”
Steven Zelditch · 1987
Earlier work this paper cites.
“The behaviour of eigenstates of arithmetic hyperbolic manifolds”
Ze\’ev Rudnick and Peter Sarnak · 1994
Earlier work this paper cites.
“Chaos and quantum thermalization”
M. Srednicki · 1994
Earlier work this paper cites.
“On the rate of quantum ergodicity. I. Upper bounds”
Steven Zelditch · 1994
Earlier work this paper cites.
“Approach to ergodicity in quantum wave functions”
B. Eckhardt, S. Fishman, J. Keating, O. Agam, J. Main and K. M\"uller · 1995
Earlier work this paper cites.
“Quantum ergodicity of eigenfunctions on PSL 2 ( 𝐙 ) \ 𝐇 2 {\rm PSL}_{2}(\mathbf{Z})\backslash\mathbf{H}^{2} ”
Wen Luo and Peter Sarnak · 1995
Earlier work this paper cites.
“Quantum unique ergodicity for parabolic maps”
J. Marklof and Z. Rudnick · 2000
Earlier work this paper cites.
“On the distribution of matrix elements for the quantum cat map”
P\"ar Kurlberg and Ze\’ev Rudnick · 2005
Earlier work this paper cites.
“High dimensional normality of noisy eigenvectors”
Jake Marcinek and Horng-Tzer Yau · 2005
Cited alongside, same era.
“Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards”
A.. Barnett · 2006
Cited alongside, same era.
“Invariant measures and arithmetic quantum unique ergodicity”
Elon Lindenstrauss · 2006
Cited alongside, same era.
“Upper bounds on the rate of quantum ergodicity”
Roman Schubert · 2006
Cited alongside, same era.
“Optimal Delocalization for Generalized Wigner Matrices”
Lucas Benigni and Patrick Lopatto · 2007
Cited alongside, same era.
“On the rate of quantum ergodicity for quantised maps”
“Joint quasimodes, positive entropy, and quantum unique ergodicity”
Shimon Brooks and Elon Lindenstrauss · 2014
Later among the works it cites.
“Quantum ergodicity on large regular graphs”
Nalini Anantharaman and Etienne Le · 2015
Later among the works it cites.
“The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case”
L\’aszl\’o Erdos and Antti Knowles · 2015
Later among the works it cites.
“From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics”
Luca D’Alessio, Yariv Kafri, Anatoli Polkovnikov and Marcos Rigol · 2016
Later among the works it cites.
“Large complex correlated Wishart matrices: the Pearcey kernel and expansion at the hard edge”
Walid Hachem, Adrien Hardy and Jamal Najim · 2016
Later among the works it cites.
“Quantum ergodicity on regular graphs”
Nalini Anantharaman · 2017
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Roman Schubert · 2008
Cited alongside, same era.
“Local semicircle law and complete delocalization for Wigner random matrices”
L\’aszl\’o Erdos, Benjamin Schlein and Horng-Tzer Yau · 2009
Cited alongside, same era.
“Mass equidistribution for Hecke eigenforms”
Roman Holowinsky and Kannan Soundararajan · 2010
Cited alongside, same era.
“Quantum unique ergodicity for SL 2 ( ℤ ) \ ℍ {\rm SL}_{2}(\mathbb{Z})\backslash\mathbb{H} ”
Kannan Soundararajan · 2010
Cited alongside, same era.
“Recent developments in mathematical quantum chaos”
Steve Zelditch · 2010
Cited alongside, same era.
“Rigidity of eigenvalues of generalized Wigner matrices”
L\’aszl\’o Erdos, Horng-Tzer Yau and Jun Yin · 2011
Cited alongside, same era.
“Functional Central Limit Theorems for Wigner Matrices”
Giorgio Cipolloni, L\’aszl\’o Erdos and Dominik Schr\"oder · 2012
Cited alongside, same era.
Later among the works it cites.
“The eigenvector moment flow and local quantum unique ergodicity”
P. Bourgade and H.-T. Yau · 2017
Later among the works it cites.
“Mesoscopic eigenvalue statistics of Wigner matrices”
Yukun He and Antti Knowles · 2017
Later among the works it cites.
“Quantitative equidistribution properties of toral eigenfunctions”
Hamid Hezari and Gabriel Rivi\‘ere · 2017
Later among the works it cites.
“Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces”
Etienne Le and Tuomas Sahlsten · 2017
Later among the works it cites.
“Eigenstate thermalization hypothesis”
J.M. Deutsch · 2018
Later among the works it cites.
“Quantum ergodicity on graphs: from spectral to spatial delocalization”
Nalini Anantharaman and Mostafa Sabri · 2019
Later among the works it cites.
“Local Kesten-McKay law for random regular graphs”
Roland Bauerschmidt, Jiaoyang Huang and Horng-Tzer Yau · 2019
Later among the works it cites.
“Random matrices with slow correlation decay”
L\’aszl\’o Erdos, Torben Kr\"uger and Dominik Schr\"oder · 2019
Later among the works it cites.
“Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices”
L. Benigni · 2020
Closest in time.
“Random band matrices in the delocalized phase I: Quantum unique ergodicity and universality”
Paul Bourgade, Horng-Tzer Yau and Jun Yin · 2020
Closest in time.
“Cusp universality for random matrices I: local law and the complex Hermitian case”
L\’aszl\’o Erdos, Torben Kr\"uger and Dominik Schr\"oder · 2020
Closest in time.
“Quantum statistical mechanics in a closed system”
J.M. Deutsch · 2046
Closest in time.