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Information, Physics, and Computation

Marc Mézard and Andrea Montanari

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and ... More


The 1RSB cavity method

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0019
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In graphical models whose factor graph has a locally tree-like structure, belief propagation may fail because variables become correlated at large distances. This phenomenon has been observed in many ... More


Random K-satisfiability

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0020
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter studies an ensemble of random satisfiability problems, ‘random K-satisfiability’ (K-SAT). Applying the 1RSB cavity method, it first derives the phase diagram in the limit of large N, in ... More


Cavity method: message-passing from a physics perspective

Marc Mézard

in Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics: Special Issue, October 2013

Published in print:
2015
Published Online:
March 2016
ISBN:
9780198743736
eISBN:
9780191803802
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198743736.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The cavity method is introduced as a heuristic framework from a physics perspective to solve probabilistic graphical models and is presented at both the replica symmetry (RS) and one-step replica ... More


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