2003/12/31 by Olivier Rivoire
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Computer science #Connection (principal bundle) #Geometry #Graph #Mathematics #Physics #Quantum mechanics #Random graph #Replica #Replica trick #Spin glass #Statistical physics #Symmetry (geometry) #Symmetry breaking #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-004-2265-9
published as Journal of Statistical Physics 117 (2004) 453
arxiv created 2004/09/21 · openalex publication_date 2004/10/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.