243 citations · 1.7k across the 42 of their papers we have counts for
4 papers · 1 filter
Random Sorting Networks
Omer Angel, Alexander E. Holroyd, Dan Romik +1
A sorting network is a shortest path from 12...n to n...21 in the Cayley graph of S_n generated by nearest-neighbour swaps. We prove that for a uniform random sorting network, as n…
Complex determinantal processes and H1 noise
Brian Rider, Balint Virag
For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinantal point processes with intensity rho dnu, where nu is the corresponding invariant measur…
Beta ensembles, stochastic Airy spectrum, and a diffusion
Jose Ramirez, Brian Rider, Balint Virag
We prove that the largest eigenvalues of the beta ensembles of random matrix theory converge in distribution to the low-lying eigenvalues of the random Schroedinger operator -d^2/d…
The noise in the circular law and the Gaussian free field
Brian Rider, Balint Virag
Fill an n x n matrix with independent complex Gaussians of variance 1/n. As n approaches infinity, the eigenvalues {z_k} converge to a sum of an H^1-noise on the unit disk and an i…