The Weak Limit of Ising Models on Locally Tree-Like Graphs

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dc.contributor.authorMontanari, Andrea
dc.contributor.authorMossel, Elchanan
dc.contributor.authorSly, Allan
dc.date2023-05-17T14:57:53.000
dc.date.accessioned2023-05-23T03:37:16Z
dc.date.available2023-05-23T03:37:16Z
dc.date.issued2012-02-01
dc.date.submitted2016-07-12T10:40:47-07:00
dc.description.abstractWe consider the Ising model with inverse temperature β and without external field on sequences of graphs G n which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weakly converges to the symmetric mixture of the Ising model with + boundary conditions and the − boundary conditions on the k-regular tree with inverse temperature β. In the case where the graphs G n are expanders we derive a more detailed understanding by showing convergence of the Ising measure conditional on positive magnetization (sum of spins) to the + measure on the tree.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/47923
dc.legacy.articleid1070
dc.legacy.fields10.1007/s00440-010-0315-6
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1070&context=statistics_papers&unstamped=1
dc.rights<p>The final publication is available at Springer via <a href="http://dx.doi.org/[10.1007/s00440-010-0315-6">http://dx.doi.org/[10.1007/s00440-010-0315-6</a>.</p>
dc.source.beginpage31
dc.source.endpage51
dc.source.issue527
dc.source.issue1
dc.source.journalStatistics Papers
dc.source.journaltitleProbability Theory and Related Fields
dc.source.peerreviewedtrue
dc.source.statuspublished
dc.source.volume152
dc.subject.otherStatistics and Probability
dc.titleThe Weak Limit of Ising Models on Locally Tree-Like Graphs
dc.typeArticle
digcom.contributor.authorMontanari, Andrea
digcom.contributor.authorMossel, Elchanan
digcom.contributor.authorSly, Allan
digcom.identifierstatistics_papers/527
digcom.identifier.contextkey8825970
digcom.identifier.submissionpathstatistics_papers/527
digcom.typearticle
dspace.entity.typePublication
upenn.schoolDepartmentCenterStatistics Papers
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