Information, Physics, and Computation

Information, Physics, and Computation

by Marc Mezard, Andrea Montanari
     
 

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 coding/information theory. It is accessible to graduate students and researchers without a specific training in any of these fields. The selected topics include spin glasses, error

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Overview

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 coding/information theory. It is accessible to graduate students and researchers without a specific training in any of these fields. The selected topics include spin glasses, error correcting codes, satisfiability, and are central to each field. The approach focuses on large random instances, adopting a common probabilistic formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to study phase transitions.

Product Details

ISBN-13:
9780198570837
Publisher:
Oxford University Press, USA
Publication date:
03/27/2009
Series:
Oxford Graduate Texts Series
Pages:
560
Product dimensions:
7.00(w) x 9.60(h) x 4.30(d)

Table of Contents

Pt. I Background

1 Introduction to information theory 3

2 Statistical physics and probability theory 23

3 Introduction to combinatorial optimization 47

4 A probabilistic toolbox 65

Pt. II Independence

5 The random energy model 93

6 The random code ensemble 107

7 Number partitioning 131

8 Introduction to replica theory 145

Pt. III Models on Graphs

9 Factor graphs and graph ensembles 173

10 Satisfiability 197

11 Low-density parity-check codes 219

12 Spin glasses 241

13 Bridges: Inference and the Monte Carlo method 267

Pt. IV Short-Range Correlations

14 Belief propagation 291

15 Decoding with belief propagation 327

16 The assignment problem 355

17 Ising models on random graphs 381

Pt. V Long-Range Correlations

18 Linear equations with Boolean variables 403

19 The 1RSB cavity method 429

20 Random K-satisfiability 467

21 Glassy states in coding theory 493

22 An ongoing story 517

App. A Symbols and notation 541

References 547

Index 565

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