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Media type:
E-Article
Title:
MIXING TIME OF METROPOLIS CHAIN BASED ON RANDOM TRANSPOSITION WALK CONVERGING TO MULTIVARIATE EWENS DISTRIBUTION
Contributor:
Jiang, Yunjiang
imprint:
Institute of Mathematical Statistics, 2015
Published in:The Annals of Applied Probability
Language:
English
ISSN:
1050-5164
Origination:
Footnote:
Description:
<p>We prove sharp rates of convergence to the Ewens equilibrium distribution for a family of Metropolis algorithms based on the random transposition shuffle on the symmetric group, with starting point at the identity. The proofs rely heavily on the theory of symmetric Jack polynomials, developed initially by Jack [Proc. Roy. Soc. Edinburgh Sect. A 69 (1970/1971) 1–18], Macdonald [Symmetric Functions and Hall Polynomials (1995) New York] and Stanley [Adv. Math. 77 (1989) 76–115]. This completes the analysis started by Diaconis and Hanlon in [Contemp. Math. 138 (1992) 99–117]. In the end we also explore other integrable Markov chains that can be obtained from symmetric function theory.</p>