{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T01:36:10Z","timestamp":1723253770493},"reference-count":24,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,4]],"date-time":"2012-04-04T00:00:00Z","timestamp":1333497600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2013,1]]},"abstract":"Abstract<\/jats:title>The theory of convergent graph sequences has been worked out in two extreme cases, dense graphs and bounded degree graphs. One can define convergence in terms of counting homomorphisms from fixed graphs into members of the sequence (left\u2010convergence), or counting homomorphisms into fixed graphs (right\u2010convergence). Under appropriate conditions, these two ways of defining convergence was proved to be equivalent in the dense case by Borgs, Chayes, Lov\u00e1sz, S\u00f3s and Vesztergombi. In this paper a similar equivalence is established in the bounded degree case, if the set of graphs in the definition of right\u2010convergence is appropriately restricted.<\/jats:p>In terms of statistical physics, the implication that left convergence implies right convergence means that for a left\u2010convergent sequence, partition functions of a large class of statistical physics models converge. The proof relies on techniques from statistical physics, like cluster expansion and Dobrushin Uniqueness. \u00a9 2012 Wiley Periodicals, Inc. Random Struct. 2012<\/jats:p>","DOI":"10.1002\/rsa.20414","type":"journal-article","created":{"date-parts":[[2012,4,4]],"date-time":"2012-04-04T17:20:42Z","timestamp":1333560042000},"page":"1-28","source":"Crossref","is-referenced-by-count":52,"title":["Left and right convergence of graphs with bounded degree"],"prefix":"10.1002","volume":"42","author":[{"given":"Christian","family":"Borgs","sequence":"first","affiliation":[]},{"given":"Jennifer","family":"Chayes","sequence":"additional","affiliation":[]},{"given":"Jeff","family":"Kahn","sequence":"additional","affiliation":[]},{"given":"L\u00e1szl\u00f3","family":"Lov\u00e1sz","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,4]]},"reference":[{"key":"e_1_2_7_2_2","unstructured":"M.Ab\u00e9rt T.Hubai Benjamini\u2010Schramm convergence and the distribution of chromatic roots for sparse graphs. 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