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Information, Physics, and Computation$
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Marc Mézard and Andrea Montanari

Print publication date: 2009

Print ISBN-13: 9780198570837

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780198570837.001.0001

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A probabilistic toolbox

A probabilistic toolbox

(p.65) 4 A probabilistic toolbox
Information, Physics, and Computation

Marc Mézard

Andrea Montanari

Oxford University Press

The three fields that form the subject of this book all deal with large sets of random variables. Not surprisingly, they possess common underlying structures and techniques. This chapter describes some of them, insisting on the mathematical structures. It discusses on one hand large deviations, Sanov's theorem, and asymptotic equipartition. On the other hand, it introduces Markov chains for Monte Carlo computations, and its application to optimization with simulated annealing.

Keywords:   large deviations, Sanov, asymptotic equipartition, Monte Carlo, Markov chain, simulated annealing

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