منابع مشابه
Rapid Mixing in Markov Chains
A wide class of "counting" problems have been studied in Computer Science. Three typical examples are the estimation of (i) the permanent of an n x n 0-1 matrix, (ii) the partition function of certain n— particle Statistical Mechanics systems and (iii) the volume of an n— dimensional convex set. These problems can be reduced to sampling from the steady state distribution of implicitly defined M...
متن کاملMarkov Chains and Mixing Times
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.
متن کاملMarkov 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...
متن کاملMarkov Chains and Mixing Times
Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
متن کاملMarkov chain mixing and coupling
Recall from Lecture 2: Definition 0.1. Let S be a countable set and (X n) a sequence of random variables taking values in S. We say that (X n) is a Markov chain if it has the Markov property.
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2016
ISSN: 0895-4801,1095-7146
DOI: 10.1137/15m1022045