Semicircular elements: free probabilistic approaches (Ilwoo Cho - St Ambrose University)

In this talk, we briefly review the combinatorial free probability theory of Speicher, and consider the semicircular law from a free probabilistic point of view. The (free probabilistic) semicircular law is the free distribution of a so-called semicircular element, which is a free random variable (or an operator) of a topological *-probability space (resp., of a topological *-algebra) having free moments determined by the Catalan numbers. We are interested in how to construct such semicircular elements for fixed mutually-orthogonal integer-many projections in a C*-algebra. As an application, we discuss how to construct semicircular elements from p-adic analysis.

When 4:00 pm to 5:00 pm on Thursday, March 22, 2018
Location 111 Cummington Mall, Room 148