Mixing time for a random walk on rooted trees.
Fulman, Jason (2009)
The Electronic Journal of Combinatorics [electronic only]
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Fulman, Jason (2009)
The Electronic Journal of Combinatorics [electronic only]
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Mariusz Górajski (2009)
Annales UMCS, Mathematica
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In this paper we consider an absorbing Markov chain with finite number of states. We focus especially on random walk on transient states. We present a graph reduction method and prove its validity. Using this method we build algorithms which allow us to determine the distribution of time to absorption, in particular we compute its moments and the probability of absorption. The main idea used in the proofs consists in observing a nondecreasing sequence of stopping times. Random walk on...
Diaconis, Persi, Holmes Susan (2002)
Electronic Journal of Probability [electronic only]
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Palacios, José Luis (2009)
Journal of Probability and Statistics
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Hunter, Jeffrey J. (1991)
Journal of Applied Mathematics and Stochastic Analysis
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Fill, James Allen, Huber, Mark L. (2010)
Electronic Journal of Probability [electronic only]
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Hans C. Andersen, Persi Diaconis (2007)
Journal de la société française de statistique
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We present a generalization of hit and run algorithms for Markov chain Monte Carlo problems that is ‘equivalent’ to data augmentation and auxiliary variables. These algorithms contain the Gibbs sampler and Swendsen-Wang block spin dynamics as special cases. The unification allows theorems, examples, and heuristics developed in one domain to illuminate parallel domains.
Persi Diaconis (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Kalashnikov, Vladimir V. (1994)
Journal of Applied Mathematics and Stochastic Analysis
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Shi, Zhiyan, Yang, Weiguo (2009)
Journal of Inequalities and Applications [electronic only]
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Piotr Pokarowski (1999)
Applicationes Mathematicae
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This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.