95 citations · 433 across the 36 of their papers we have counts for
40 papers
Zeros of random polynomials undergoing the heat flow
Brian C. Hall, Ching-Wei Ho, Jonas Jalowy +1
We investigate the evolution of the empirical distribution of the complex roots of high-degree random polynomials, when the polynomial undergoes the heat flow. In one prominent exa…
The heat flow, GAF, and SL(2;R)
Brian Hall, Ching-Wei Ho, Jonas Jalowy +1
We establish basic properties of the heat flow on entire holomorphic functions that have order at most 2. We then look specifically at the action of the heat flow on the Gaussian a…
The heat flow conjecture for polynomials and random matrices
Brian C. Hall, Ching-Wei Ho
We study the evolution of the roots of a polynomial of degree , when the polynomial itself is evolving according to the heat flow. We propose a general conjecture for the large-…
The Brown measure of a family of free multiplicative Brownian motions
Brian C. Hall, Ching-Wei Ho
We consider a family of free multiplicative Brownian motions parametrized by a real variance parameter and a complex covariance parameter We compute the Brown me…
The Brown measure of the sum of a self-adjoint element and an imaginary multiple of a semicircular element
Brian C. Hall, Ching-Wei Ho
We compute the Brown measure of , where is a free semicircular Brownian motion and is a freely independent self-adjoint element that is not a multiple…
PDE methods in random matrix theory
Brian C. Hall
This article begins with a brief review of random matrix theory, followed by a discussion of how the large- limit of random matrix models can be realized using operator algebras…