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Separation Cutoffs for Random Walk on Irreducible Representations
Jason Fulman
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA
fulman@usc.edu
Annals of Combinatorics 14 (3) pp.319-337 September, 2010
AMS Subject Classification: 60C05, 20P05
Abstract:

Random walk on the irreducible representations of the symmetric and general linear groups is studied. A separation distance cutoff is proved and the exact separation distance asymptotics are determined. A key tool is a method for writing the multiplicities in the Kronecker tensor powers of a fixed representation as a sum of non-negative terms. Connections are made with the Lagrange-Sylvester interpolation approach to Markov chains.

Keywords: Markov chain, cutoff phenomenon, irreducible representation, separation distance, Lagrange-Sylvester interpolation

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