منابع مشابه
Cutoff for Samples of Markov Chains
We study the convergence to equilibrium of n−samples of independent Markov chains in discrete and continuous time. They are defined as Markov chains on the n−fold Cartesian product of the initial state space by itself, and they converge to the direct product of n copies of the initial stationary distribution. Sharp estimates for the convergence speed are given in terms of the spectrum of the in...
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A sequence of Markov chains is said to exhibit cutoff if the convergence to stationarity in total variation distance is abrupt. We prove a necessary and sufficient condition for cutoff in reversible lazy chains in terms of concentration of hitting time of certain sets of large stationary measure. (Previous works of Aldous, Oliviera, Sousi and the speaker established a less precise connection be...
متن کاملThe cutoff phenomenon in finite Markov chains.
Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to ...
متن کاملTaylor Expansion for the Entropy Rate of Hidden Markov Chains
We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...
متن کاملThe Rate of Rényi Entropy for Irreducible Markov Chains
In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.
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ژورنال
عنوان ژورنال: ESAIM: Probability and Statistics
سال: 1999
ISSN: 1292-8100,1262-3318
DOI: 10.1051/ps:1999104