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math.PR2022
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…
math.PR2020
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…
math.PR2019
A central limit theorem for integrals of random waves
Matthew de Courcy-Ireland, Marius Lemm
We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of arbit…