MIXING TIME OF METROPOLIS CHAIN BASED ON RANDOM TRANSPOSITION WALK CONVERGING TO MULTIVARIATE EWENS DISTRIBUTION
成果类型：
Article
署名作者：
Jiang, Yunjiang
署名单位：
Stanford University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/14-AAP1031
发表日期：
2015
页码：
1581-1615
关键词：
摘要：
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.