On mean recurrence times of Markov chains and spanning tree invariants
نویسندگان
چکیده
منابع مشابه
Markov chains and mixing times
For our purposes, a Markov chain is a (finite or countable) collection of states S and transition probabilities pij, where i, j ∈ S. We write P = [pij] for the matrix of transition probabilities. Elements of S can be interpreted as various possible states of whatever system we are interested in studying, and pij represents the probability that the system is in state j at time n+ 1, if it is sta...
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Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
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This paper introduces the idea of a Markov chain, a random process which is independent of all states but its current one. We analyse some basic properties of such processes, introduce the notion of a stationary distribution, and examine methods of bounding the time it takes to become close to such a distribution.
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1
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The question of recurrence and transience of branching Markov chains is more subtle than for ordinary Markov chains; they can be classified in transience, weak recurrence, and strong recurrence. We review criteria for transience and weak recurrence and give several new conditions for weak recurrence and strong recurrence. These conditions make a unified treatment of known and new examples possi...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.06.033