Mixing Time of Metropolis Chain Based on Random Transposition Walk Converging to Multivariate Ewens Distribution

Details Mixing Time of Metropolis Chain Based on Random Transposition Walk Converging to Multivariate Ewens Distribution Mixing Time of Metropolis Chain Based on Random Transposition Walk Converging to Multivariate Ewens Distribution

2012-04-07

arxiv.org/abs/1204.1671v1

Mathematics

Probability

Scientific paper

We prove sharp rates of convergence to the Ewens equilibrium distribution for a family of Metropolis algorithm based on the random transposition shuffle on the symmetric group, with starting point at the identity or at a random n-cycle. The proofs rely heavily on the theory of symmetric Jack polynomials, developed initially by Jack, Macdonald, and Stanley. This completes the analysis started by Diaconis and Hanlon. In the end we also explore other integrable Markov chains that can be obtained from symmetric function theory.

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