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Finite Markov Chains and Algorithmic Applications (2001) [46 citations — 1 self]

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@INPROCEEDINGS{Häggström01finitemarkov,
    author = {Olle Häggström and Matematisk Statistik},
    title = {Finite Markov Chains and Algorithmic Applications},
    booktitle = {in London Mathematical Society Student Texts},
    year = {2001},
    publisher = {Cambridge University Press}
}

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CONTENTS 0 PREFACE 3 1 BASICS OF PROBABILITY THEORY 5 2 MARKOV CHAINS 12 3 COMPUTER SIMULATION OF MARKOV CHAINS 19 4 IRREDUCIBLE AND APERIODIC MARKOV CHAINS 25 5 STATIONARY DISTRIBUTIONS 30 6 REVERSIBLE MARKOV CHAINS 41 7 MARKOV CHAIN MONTE CARLO 46 8 FAST CONVERGENCE OF MCMC ALGORITHMS 54 9 APPROXIMATE COUNTING 63 10 THE PROPP--WILSON ALGORITHM 74 11 PROPP--WILSON WITH READ-ONCE RANDOMNESS 82 12 SIMULATED ANNEALING 88 13 FURTHER READING 96 1 2 0 PREFACE The first version of these lecture notes was composed for a new course on randomized algorithms at Chalmers University of Technology, in the spring semester 2000. The amount of material contained therein was not quite enough for an entire course, and the idea was to use these notes together with the book "Randomized Algorithms" by Motwani & Raghavan [MR]. The current version of 2001 has now, with the addition of three more chapters (Chapters 8, 9 and 11), expanded into something more "course-sized", bu

Citations

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1516	The Art of Computer Programming – Knuth - 1968
1309	Randomized algorithms – Motwani, Raghavan - 1995
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278	Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Structures and Algorithms – Propp, Wilson - 1996
168	Lectures on the coupling method – Lindvall - 2002
153	Markov Chains: Gibbs fields, Monte Carlo simulation, and queues – Brémaud - 1999
150	Markov Chains – Norris - 1997
140	Algorithms for Random Generation and Counting: a Markov Chain Approach – Sinclair
83	A very simple algorithm for estimating the number of k-colourings of a low-degree graph, Random Structures and Algorithms – Jerrum - 1995
28	Fast convergence of the Glauber dynamics for sampling independent sets. Random Structures and Algorithms – Luby, Vigoda - 1999
22	How to couple from the past using a read-once source of randomness. Random Structures and Algorithms – Wilson - 1999
16	On exact simulation of Markov random fields using coupling from the past – Häggström, Nelander - 1999
9	A guide to exact simulation – Dimakos - 2000
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2	Pseudorandomness – Goldreich - 1999
2	Slumpvandringar och likstromskretsar – Haggstrom - 2000
1	Markovprocesser, Lunds Universitet och Lunds Tekniska Hogskola, Institutionen for matematisk statistik – Ryd'en - 1996
1	Topics in Contemporary Probability and its Applications – Snell - 1994