The Annals of Probability

Covering Problems for Markov Chains

Peter Matthews

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Abstract

Upper and lower bounds are given on the moment generating function of the time taken by a Markov chain to visit at least $n$ of $N$ selected subsets of its state space. An example considered is the class of random walks on the symmetric group that are constant on conjugacy classes. Application of the bounds yields, for example, the asymptotic distribution of the time taken to see all $N!$ arrangements of $N$ cards as $N\rightarrow\infty$ for certain shuffling schemes.

Article information

Source
Ann. Probab., Volume 16, Number 3 (1988), 1215-1228.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991686

Digital Object Identifier
doi:10.1214/aop/1176991686

Mathematical Reviews number (MathSciNet)
MR942764

Zentralblatt MATH identifier
0712.60076

JSTOR
links.jstor.org

Subjects
Primary: 60G17: Sample path properties
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

Keywords
Symmetric group random shuffle random allocation

Citation

Matthews, Peter. Covering Problems for Markov Chains. Ann. Probab. 16 (1988), no. 3, 1215--1228. doi:10.1214/aop/1176991686. https://projecteuclid.org/euclid.aop/1176991686


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