Markov Chains and Mixing Times
نویسندگان
چکیده
Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
منابع مشابه
Markov chains and mixing times ( part 2 - coupling )
This week’s post continues last week’s discussion of Markov chains and mixing times, and introduces the idea of coupling as a method for estimating mixing times. We remark that some nice notes on the subject of coupling (and others) can be found on Steve Lalley’s web page – of particular relevance for our purposes here are the notes on “Convergence rates of Markov chains”. A more thorough and c...
متن کاملMathematical Aspects of Mixing Times in Markov Chains Mathematical Aspects of Mixing Times in Markov Chains
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متن کاملMixing Times for Uniformly Ergodic Markov Chains
Consider the class of discrete time, general state space Markov chains which satist)' a "'uniform ergodicity under sampling" condition. There are many ways to quantify the notion of "mixing time", i.e., time to approach stationarity from a worst initial state. We prove results asserting equivalence (up to universal constants) of different quantifications of mixing time. This work combines three...
متن کاملThe University of Chicago Robust Mixing a Dissertation Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy Department of Computer Science by Murali Krishnan Ganapathy
How many times should a card shuffler shuffle to get the cards shuffled? Convergence rate questions like these are central to the theory of finite Markov Chains and arise in diverse fields including Physics, Computer Science as well as Biology. This thesis introduces two new approaches to estimating mixing times: robust mixing time of a Markov Chain and Markovian product of Markov Chains. The “...
متن کاملThe University of Chicago Robust Mixing a Dissertation Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy Department of Computer Science by Murali Krishnan Ganapathy
How many times should a card shuffler shuffle to get the cards shuffled? Convergence rate questions like these are central to the theory of finite Markov Chains and arise in diverse fields including Physics, Computer Science as well as Biology. This thesis introduces two new approaches to estimating mixing times: robust mixing time of a Markov Chain and Markovian product of Markov Chains. The “...
متن کاملThe Distribution of Mixing times in Markov Chains
The distribution of the “mixing time” or the “time to stationarity” in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the Markov chain. Expressions for the probability generating function, and hence the probability distribution of the mixing time starting in state i are derived an...
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