Orthogonality and probability: mixing times
نویسندگان
چکیده
منابع مشابه
Orthogonality and probability: mixing times
We produce the first example of bounding total variation distance to stationarity and estimating mixing times via orthogonal polynomials diagonalization of discrete reversible Markov chains, the Karlin-McGregor approach.
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The critical issue in the complexity of Markov chain sampling techniques has been \mixing time", the number of steps of the chain needed to reach its stationary distribution. It turns out that there are many ways to deene mixing time|more than a dozen are considered here|but they fall into a small number of classes. The parameters in each class lie within constant multiples of one another, inde...
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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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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2010
ISSN: 1083-589X
DOI: 10.1214/ecp.v15-1525