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Universal Eigenvalue Statistics for Dynamically Defined Matrices
Arka Adhikari, Marius Lemm
We consider dynamically defined Hermitian matrices generated from orbits of the doubling map. We prove that their spectra fall into the GUE universality class from random matrix th…
A Local Law for Singular Values from Diophantine Equations
Arka Adhikari, Marius Lemm
We introduce the random matrices $$ X_{j,k}=\exp\left(2πi \sum_{q=1}^d\ ω_{j,q} k^q\right) \quad \text{with } \{ω_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \te…
Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field
Arka Adhikari, Christian Brennecke
We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inve…
Spin Distributions for Generic Spherical Spin Glasses
Arka Adhikari
This paper investigates p-spin distributions for a generic spherical p-spin model; we give a representation of spin distributions in terms of a stochastic process. In order to do t…
Dyson Brownian Motion for General and Potential at the Edge
Arka Adhikari, Jiaoyang Huang
In this paper, we compare the solutions of Dyson Brownian motion with general and potential and the associated McKean-Vlasov equation near the edge. Under suitable conditio…
The Edge Universality of Correlated Matrices
Arka Adhikari, Ziliang Che
We consider a Gaussian random matrix with correlated entries that have a power law decay of order and prove universality for the extreme eigenvalues. A local law is proved us…