Olivier Rivoire J. Stat. Mech. (2005) P07004 doi:10.1088/1742-5468/2005/07/P07004
Olivier Rivoire
Show affiliationsA 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.
E-print Number: cond-mat/0506164
Cited: by |
Refers: to
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
02.10.Ox Combinatorics; graph theory
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
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.)
Issue 07 (July 2005)
Received 7 June 2005, accepted for publication 29 June 2005
Published 14 July 2005
Olivier Rivoire J. Stat. Mech. (2005) P07004
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