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Eigenstate Thermalization Hypothesis for Generalized Wigner Matrices  Arka Adhikari
; Sofiia Dubova
; Changji Xu
; Jun Yin
;  Date: 
1 Feb 2023  Abstract:  In this paper, we extend results of Eigenvector Thermalization to the case of
generalized Wigner matrices. Analytically, the central quantity of interest
here are multiresolvent traces, such as $Lambda_A:= frac{1}{N} ext{Tr }{
GAGA}$. In the case of Wigner matrices, as in
cite{cipollonierdosschroder2021}, one can form a selfconsistent equation
for a single $Lambda_A$. There are multiple difficulties extending this logic
to the case of general covariances. The correlation structure prevents us from
deriving a selfconsistent equation for a single matrix $A$; this is due to the
introduction of new terms that are quite distinct from the form of $Lambda_A$.
We find a way around this by carefully splitting these new terms and writing
them as sums of $Lambda_B$, for matrices $B$ obtained by modifying $A$ using
the covariance matrix. The result is a system of selfconsistent equations
relating families of deterministic matrices. Our main effort in this work is to
derive and analyze this system of selfconsistent equations.  Source:  arXiv, 2302.00157  Services:  Forum  Review  PDF  Favorites 


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