## The Annals of Probability

### Covering Problems for Markov Chains

Peter Matthews

#### 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

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