Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BK-type inequalities and generalized random-cluster representations   Recently, van den Berg and Jonasson gave the first substantial extension of
the BK inequality for non-product measures: they proved that, for k-out-of-n
measures, the probability that two increasing events occur disjointly is at
most the product of the two individual probabilities.
  We show several other extensions and modifications of the BK inequality.In
particular, we prove that the antiferromagnetic Ising Curie-Weiss model
satisfies the BK inequality for all increasing events. We prove that this also
holds for the Curie-Weiss model with three-body interactions under the
so-called Negative Lattice Condition. For the ferromagnetic Ising model we show
that the probability that two events occur `cluster-disjointly' is at most the
product of the two individual probabilities, and we give a more abstract form
of this result for arbitrary Gibbs measures.
  The above cases are derived from a general abstract theorem whose proof is
based on an extension of the Fortuin-Kasteleyn random-cluster representation
for all probability distributions and on a `folding procedure' which
generalizes an argument of D. Reimer.

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The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ