Separated-occurrence inequalities for dependent percolation and Ising models

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dc.creatorAlexander, Kenneth S.
dc.date2002-10-01
dc.date.accessioned2026-07-07T04:51:25Z
dc.date.available2026-07-07T04:51:25Z
dc.descriptionSeparated-occurrence inequalities are variants for dependent lattice models of the van den Berg-Kesten inequality for independent models. They take the form $P(A \circ_r B) \leq (1 + ce^{-εr})P(A)P(B)$, where $A \circ_r B$ is the event that $A$ and $B$ occur at separation $r$ in a configuration $ω$, that is, there exist two random sets of bonds or sites separated by at least distance $r$, one set responsible for the occurrence of the event $A$ in $ω$, the other for the occurrence of $B$. We establish such inequalities for certain subcritical FK models, and for certain Ising models which are at supercritical temperature or have an external field, with $A$ and $B$ increasing or decreasing events.
dc.description38 pages, 2 figures (.eps files). See also http://math.usc.edu/~alexandr/
dc.identifierhttps://arxiv.org/abs/math/0210015
dc.identifierhttp://arxiv.org/abs/math/0210015
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65138
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35; 82B20; 82B43
dc.titleSeparated-occurrence inequalities for dependent percolation and Ising models
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