Eigenstate thermalisation hypothesis and Gaussian fluctuations for Wigner matrices
[HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 1 August 23, 2021 - August 27, 2021
Location: SLMath: Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Eigenstate Thermalisation Hypothesis And Gaussian Fluctuations For Wigner Matrices
We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix W with an optimal error inversely proportional to the square root of the dimension. This verifies a strong form of Quantum Unique Ergodicity with an optimal convergence rate and we also prove Gaussian fluctuations around this convergence. The key technical tool is a new multi-resolvent local law for Wigner ensemble and the Dyson Brownian motion for eigenvector overlaps.
|
Slides
|
Download |
Eigenstate Thermalisation Hypothesis And Gaussian Fluctuations For Wigner Matrices
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.