Sep 13, 3:30pm, Wean 8220

Sevak Mkrtchyan, CMU

The Entropy of Schur-Weyl measures

Sevak Mkrtchyan, CMU

The Entropy of Schur-Weyl measures

Abstract:

We will study local and global statistical properties of
Young diagrams with respect to a Plancherel-type family of measures
called Schur-Weyl measures and use the results to answer a question
from asymptotic representation theory. More precisely, we will solve a
variational problem to prove a limit-shape result for random Young
diagrams with respect to the Schur-Weyl measures and apply the results
to obtain logarithmic, order-sharp bounds for the dimensions of
certain representations of finite symmetric groups. We will discuss
connections with random matrix theory and combinatorics, in particular
the RSK algorithm and longest increasing subsequences.