Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shearer's measure and stochastic domination of product measures   Let G=(V,E) be a locally finite graph. Let \vec{p}\in[0,1]^V. We show that
Shearer's measure, introduced in the context of the Lovasz Local Lemma, with
marginal distribution determined by \vec{p} exists on G iff every Bernoulli
random field with the same marginals and dependency graph G dominates
stochastically a non-trivial Bernoulli product field. Additionaly we derive a
lower non-trivial uniform bound for the parameter vector of the dominated
Bernoulli product field. This generalizes previous results by Liggett,
Schonmann & Stacey in the homogeneous case, in particular on the k-fuzz of Z.
Using the connection between Shearer's measure and lattice gases with hardcore
interaction established by Scott & Sokal, we apply bounds derived from cluster
expansions of lattice gas partition functions to the stochastic domination
problem.

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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: bayes-an