Brian C. Hall

collaborators

4 papers

math.PR2026

Repeated differentiation of deterministic polynomials with asymptotically radial root distributions

Brian C. Hall, Daniel Perales

Recent works of Galligo, Najnudel, and Vu (2025) and Najnudel and Vu (2026) study repeated differentiation for polynomials of the form $P (z) = p (z^{m})$ , where $p$ is a deterministic p…

math.PR2025

Matrix Random Walks and the Lima Bean Law

Bruce K. Driver, Brian C. Hall, Ching Wei Ho +4

A matrix random walk is a stochastic process of the form $B_{k} = (I + A_{1}) \dots (I + A_{k})$ where $A_{j}$ are independent ``step'' matrices in $M_{N} (C)$ . With the right en…

math.OA2025

Spectral results for free random variables

Brian C. Hall, Ching-Wei Ho

Let $(A, tr)$ be a von Neumann algebra with a faithful, normal trace $tr : A \to C .$ For each $a \in A,$ define \[ S(λ,\va…

math.PR2025

Support of the Brown measure of a family of free multiplicative Brownian motions with non-negative initial condition

Brian C. Hall, Sorawit Eaknipitsari

We consider a family $b_{s, τ}$ of free multiplicative Brownian motions labeled by a real variance parameter $s$ and a complex covariance parameter $τ$ . We then consider the element…