Speaker: Sorawit Eaknitspari
University of Notre Dame
Will give a PhD Defense entitled:
Support of the Brown measure of free multiplicative Brownian motions freely convoluted with positive elements and its three-parameter family
Abstract: We study a family of free multiplicative Brownian motions $b_{s,\tau}$ parameterized by a real variance $s$ and a complex covariance $\tau$. We compute a support of the Brown measure $\mu_{s,\tau}$ of $hb_{s,\tau}$, where $h$ is a positive element freely independent of $b_{s,\tau}$. We find that, in the initial case $\tau =s$, outside of the region $\compconj{\Delta}_s$ the Brown measure $\mu_{s,s} = \mu\{0\}\delta_0.$ Then for the general $\tau$ case, the support $D_{s,\tau}$ is the complement of the set obtained by mapping $\compconj{\Delta}_s^c$ under $f_{s-\tau}$ and outside $D_{s,\tau}$ the Brown measure $ \mu_{s,\tau}$ is also $\mu\{0\}\delta_0.$
Date: 03-19-2024
Time: 1:00 pm
Location: 229 Hayes-Healy Bldg