Limits of discrete distributions and Gibbs measures on random graphs
| Autor: | Amin Coja-Oghlan, Kathrin Skubch, Will Perkins |
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| Rok vydání: | 2015 |
| Předmět: |
Random graph
Discrete mathematics Work (thermodynamics) 010102 general mathematics Probability (math.PR) Szemerédi regularity lemma 0102 computer and information sciences 01 natural sciences Combinatorics 010201 computation theory & mathematics Convergence (routing) FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Graph (abstract data type) Probability distribution Combinatorics (math.CO) 0101 mathematics Representation (mathematics) Mathematics - Probability Factor graph Mathematics |
| DOI: | 10.48550/arxiv.1512.06798 |
| Popis: | Building upon the theory of graph limits and the Aldous–Hoover representation and inspired by Panchenko’s work on asymptotic Gibbs measures [Annals of Probability 2013], we construct continuous embeddings of discrete probability distributions. We show that the theory of graph limits induces a meaningful notion of convergence and derive a corresponding version of the Szemeredi regularity lemma. Moreover, complementing recent work Bapst et al. (2015), we apply these results to Gibbs measures induced by sparse random factor graphs and verify the “replica symmetric solution” predicted in the physics literature under the assumption of non-reconstruction. |
| Databáze: | OpenAIRE |
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