Smooth linear eigenvalue statistics on random covers of compact hyperbolic surfaces -- A central limit theorem and almost sure RMT statistics

Autor:	Maoz, Yotam
Rok vydání:	2023
Předmět:	Mathematics - Spectral Theory Mathematical Physics Mathematics - Dynamical Systems Mathematics - Geometric Topology Mathematics - Number Theory Mathematics - Probability 81Q50 (Primary) 11F72 58J50 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We study smooth linear spectral statistics of twisted Laplacians on random $n$-covers of a fixed compact hyperbolic surface $X$. We consider two aspects of such statistics. The first is the fluctuations of such statistics in a small energy window around a fixed energy level when averaged over the space of all degree $n$ covers of $X$. The second is the energy variance of a typical surface. In the first case, we show a central limit theorem. Specifically, we show that the distribution of such fluctuations tends to a Gaussian with variance given by the corresponding quantity for the Gaussian Orthogonal/Unitary Ensemble (GOE/GUE). In the second case, we show that the energy variance of a typical random $n$-cover is that of the GOE/GUE. In both cases, we consider a double limit where first we let $n$, the covering degree, go to $\infty$ then let $L\to \infty$ where $1/L$ is the window length. Comment: 47 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.18663 Zobrazit plný text záznamu View this record from Arxiv