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  Large Deviation Bounds for Markov Chains (1994) [11 citations — 0 self]

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by Nabil Kahale
http://www.research.att.com/~kahale/papers/markov.ps
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Abstract:

We study the fraction of time that a Markov chain spends in a given subset of states. We give an exponential bound on the probability that it exceeds its expectation by a constant factor. Our bound depends on the mixing properties of the chain, and is asymptotically optimal for a certain class of Markov chains. It beats the best previously known results in this direction. We present an application to the leader election problem. 1

Citations

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158 Reversible markov chains and random walks on graphs. monograph in preparation. [Online]. Available: http://stat-www.berkeley.edu/users/aldous/RWG/book.html – Aldous, Fill
157 Non-negative Matrices and Markov Chains – Seneta - 1981
87 Deterministic simulation in Logspace – Ajtai, Komlós, et al. - 1987
84 Random walks in a convex body and an improved volume algorithm. Random structures & algorithms – Lovasz, Simonovits - 1993
61 On the Markov chain simulation method for uniform combinatorial distributions and simulated annealing", Probability in – Aldous - 1987
50 A chernoff bound for random walks on expander graphs – Gillman - 1998
38 Security Preserving Amplification of Hardness – Goldreich, Impagliazzo, et al. - 1990
26 deterministic amplification, and weak random sources – Dispersers - 1989
19 expansion for Ramanujan graphs – Kahale, Better - 1991
11 Simple and efficient leader election in the full information model – Ostrovsky, Rajagopalan, et al. - 1994
3 A measure of the asymptotic efficiency of a hypothesis based on a sum of observations – Chernoff - 1952
2 Central limit theorems and statistical inference for finite markov chains – Hoglund - 1974
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