




















We define and study the rectangular finite free heat flow, a dynamical system on polynomials that plays the role of the heat equation in the setting of rectangular finite free probability. We show several equivalent characterizations of the evolution (including PDE and gradient flow formulations), establish basic properties of the dynamics, and determine the asymptotic distributions of the polynomial roots in the long-time and high-degree limits. We also discuss connections with Calogero-Moser systems and Dunkl processes, and we show that the rectangular finite free heat flow describes the mean curvature expansion of a family of compact Lie group orbits.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。