16 citations · 22 across the 7 of their papers we have counts for
7 papers · 1 filter
Evolution of the Stochastic Airy eigenvalues under a changing boundary
Angelica Gonzalez, Diane Holcomb
The Airy point process, originally introduced by Ramírez, Rider, and Virág, is defined as the spectrum of the stochastic Airy operator acting on a subspace of $…
The maximum deviation of the Sine counting process
Diane Holcomb, Elliot Paquette
In this paper, we consider the maximum of the counting process from its expectation. We show the leading order behavior is consistent with the predictions of log-co…
Tridiagonal Models for Dyson Brownian Motion
Diane Holcomb, Elliot Paquette
In this paper, we consider tridiagonal matrices the eigenvalues of which evolve according to -Dyson Brownian motion. This is the stochastic gradient flow on given…
The random matrix hard edge: rare events and a transition
Diane Holcomb
We study probabilities of various rare events for the limiting point process that appears at the random matrix hard edge. We also show a transition from hard edge to bulk behavior.…
Overcrowding asymptotics for the Sine_beta process
Diane Holcomb, Benedek Valkó
We give overcrowding estimates for the Sine_beta process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having at least n points in a…
Large deviations for the Sine_beta and Sch_tau processes
Diane Holcomb, Benedek Valkó
We study two one-parameter families of point processes connected to random matrices: the Sine_beta and Sch_tau processes. The first one is the bulk point process limit for the Gaus…