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The cavity method for large deviations

Olivier Rivoire

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A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to compute exponentially small probabilities (rate functions) over different classes of random graphs. It is illustrated with two combinatorial optimization problems, the vertex-cover and colouring problems, for which the presence of replica symmetry breaking phases is taken into account. Applications include the analysis of models on adaptive graph structures.


Keywords

random graphs, networks

disordered systems (theory)

cavity and replica method

typical-case computational complexity

 

E-print Number: cond-mat/0506164

Cited: by |

Refers: to

PACS

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

02.10.Ox Combinatorics; graph theory

05.70.-a Thermodynamics

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

05.20.-y Classical statistical mechanics

MSC

90C27 Combinatorial optimization

82D30 Random media, disordered materials (including liquid crystals and spin glasses)

82B30 Statistical thermodynamics (See also 80-XX)

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.)

05C80 Random graphs

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 07 (July 2005)

Received 7 June 2005, accepted for publication 29 June 2005

Published 14 July 2005



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