243 citations · 1.7k across the 42 of their papers we have counts for
5 papers · 2 filters
Brownian motion as limit of the interchange process
Mustazee Rahman, Balint Virag
We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on path graphs converges weakly to the deterministic measure o…
Geometry of Permutation Limits
Mustazee Rahman, Balint Virag, Mate Vizer
This paper initiates a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic behaviour of random sorting n…
Eigenvectors of the critical 1-dimensional random Schroedinger operator
Ben Rifkind, Balint Virag
The purpose of this paper is to understand in more detail the shape of the eigenvectors of the random Schroedinger operator H = Delta+V. Here Delta is the discrete Laplacian and V…
The Sine operator
Benedek Valkó, Bálint Virág
We show that Sine, the bulk limit of the Gaussian -ensembles is the spectrum of a self-adjoint random differential operator \[ f\to 2 {R_t^{-1}} \left[ \begin{array}{cc} 0 &…
Dyson's spike for random Schroedinger operators and Novikov-Shubin invariants of groups
Marcin Kotowski, Bálint Virág
We study Schroedinger operators with random edge weights and their expected spectral measures near zero. We prove that the measure exhibits a spike of the form $μ_H(-\varepsi…