Zeros of Polynomial Powers under the Heat Flow

by Antonia Höfert (Universität Paderborn)

Thursday Jul 16, 2026, 2:15 PM → 4:15 PM Europe/Berlin

D5-153 (UHG)

The semicircle law is a central object in e.g. random matrix theory since it arises as the limiting distribution of the eigenvalues of random symmetric matrices. In this talk, we study the evolution of zeros of polynomial powers undergoing the heat flow by using the saddle point method. We analyze the discovered limiting measure for small and large values of the time parameter respectively, and show that, after proper rescaling, we recover the semicircle distribution in the limit. Further, we give a PDE perspective for the logarithmic potential and Stieltjes transform corresponding to the limiting measure, which we will describe more explicitly along the way.