منابع مشابه
Dependent random graphs and spatial
We extend certain exponential decay results of subcritical percolation to a class of locally dependent random graphs, introduced by Kuulasmaa as models for spatial epidemics on Z d. In these models, infected individuals eventually die (are removed) and are not replaced. We combine these results with certain continuity and re-scaling arguments in order to improve our knowledge of the phase diagr...
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Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years, considerable progress has been achieved by viewing these distributions as Gibbs measures and applying to their study heuristic tools from statistical physics. We review...
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In a random graph with a spatial embedding, the probability of linking to a particular vertex v decreases with distance, but the rate of decrease may depend on the particular vertex v, and on the direction in which the distance increases. In this article, we consider the question when the embedding can be chosen to be uniform, so the probability of a link between two vertices depends only on th...
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We study the strong spatial mixing (decay of correlation) property of proper q-colorings of random graphG(n, d/n) with a fixed d. The strong spatial mixing of coloring and related models have been extensively studied on graphs with bounded maximum degree. However, for typical classes of graphs with bounded average degree, such as G(n, d/n), an easy counterexample shows that colorings do not exh...
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We model physical systems with \hard constraints" by the space Hom(G; H) of homomor-phisms from a locally nite graph G to a xed nite constraint graph H. Two homomorphisms are deemed to be adjacent if they diier on a single site of G. We investigate what appears to be a fundamental dichotomy of constraint graphs, by giving various characterizations of a class of graphs that we call dismantlable....
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2018
ISSN: 1050-5164
DOI: 10.1214/17-aap1316