Open Access
July, 1988 Covering Problems for Markov Chains
Peter Matthews
Ann. Probab. 16(3): 1215-1228 (July, 1988). DOI: 10.1214/aop/1176991686


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.


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Peter Matthews. "Covering Problems for Markov Chains." Ann. Probab. 16 (3) 1215 - 1228, July, 1988.


Published: July, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0712.60076
MathSciNet: MR942764
Digital Object Identifier: 10.1214/aop/1176991686

Primary: 60G17
Secondary: 60B15 , 60J10

Keywords: random allocation , random shuffle , Symmetric group

Rights: Copyright © 1988 Institute of Mathematical Statistics

Vol.16 • No. 3 • July, 1988
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