1999/05/31 by Giorgio Parisi, Federico Ricci-Tersenghi · 1 citation
Mathematics · Physics and Astronomy · #Distribution (mathematics) #Infinity #Mutual information #Probability distribution #Property (philosophy) #Replica #Simple (philosophy) #Stochastic process #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #advanced mathematical theories #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/33/1/307
published as J. Phys. A 33, 113 (2000). · 13 pages, 1 figure
arxiv created 1999/12/10 · openalex publication_date 1999/12/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we show that in systems where the probability distribution of the overlap is nontrivial in the infinite volume limit, the property of ultrametricity can be proved, in general, starting from two very simple and natural assumptions: each replica is equivalent to the others ( replica equivalence or stochastic stability ) and all the mutual information about a pair of equilibrium configurations is encoded in their mutual distance or overlap ( separability or overlap equivalence ).