English

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.

Keywords

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}
}
R2 v1 2026-07-22T10:58:07.762Z