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Algorithms, Combinatorics and Optimization Seminar
Carnegie Mellon University Title: 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. Date: Thursday, September 13, 2012 Time: 3:30 pm Location: WeH 8220 Submitted by: Loh |