Speaker: Ken Dykema
Affiliation: Texas A&M University
Title: Free entropy dimension in amalgamated free products.
Time and Place: Thursday, September 14, 3:00-3:55pm, Milner 317.
Abstract:
We will discuss the free convolution semigroups of Nica and Speicher and,
as a (surprisingly not necessarily particular) case, the free Brownian
motion from an analytic point of view. We start by briefly reviewing
properties of measures belonging to such semigroups and comparing them
with properties of measures which are a free convolution with a
semicircular distribution (or more generally, with a freely infinitely
divisible distribution), as they were determined by Biane. Using some simple
analytical tools, we prove continuity with respect to the time
variable at the origin in the topology of a.e. convergence.
The behavior of free additive convolution and of free multiplicative
convolution of measures on the positive half-line will be seen to be very
similar.
Part of the results presented are joint work with Hari Bercovici, and part
are derived from ongoing joint work with Alice Guionnet and Andrei
Okounkov.