Properties of atypical graphs from negative complexities
Statistical Mechanics
2009-11-10 v2 Disordered Systems and Neural Networks
Abstract
The one-step replica symmetry breaking cavity method is proposed as a new tool to investigate large deviations in random graph ensembles. The procedure hinges on a general connection between negative complexities and probabilities of rare samples in spin-glass like models. This relation between large deviations and replica theory is explicited on different models where it is confronted to direct combinatorial calculations.
Cite
@article{arxiv.cond-mat/0312501,
title = {Properties of atypical graphs from negative complexities},
author = {Olivier Rivoire},
journal= {arXiv preprint arXiv:cond-mat/0312501},
year = {2009}
}