ISING MODELS ON LOCALLY TREE-LIKE GRAPHS
成果类型：
Article
署名作者：
Dembo, Amir; Montanari, Andrea
署名单位：
Stanford University; Stanford University; Stanford University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/09-AAP627
发表日期：
2010
页码：
565-592
关键词：
摘要：
We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the cavity prediction for the limiting free energy per spin is correct for any positive temperature and external field. Further, local marginals can be approximated by iterating a set of mean field (cavity) equations. Both results are achieved by proving the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on the appropriate infinite random tree.
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