Shearer’s Measure and Stochastic Domination of Product Measures

Christoph Temmel ()
Additional contact information
Christoph Temmel: Technische Universität Graz

Journal of Theoretical Probability, 2014, vol. 27, issue 1, 22-40

Abstract: Abstract 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 Lovász Local Lemma, with marginal distribution determined by $\vec{p}$ , exists on G if and only if every Bernoulli random field with the same marginals and dependency graph G dominates stochastically a non-trivial Bernoulli product field. Additionally, we derive a non-trivial uniform lower bound for the parameter vector of the dominated Bernoulli product field. This generalises previous results by Liggett, Schonmann, and Stacey in the homogeneous case, in particular on the k-fuzz of ℤ. Using the connection between Shearer’s measure and a hardcore lattice gas established by Scott and Sokal, we transfer bounds derived from cluster expansions of lattice gas partition functions to the stochastic domination problem.

Keywords: Stochastic domination; Lovász Local Lemma; Product measure; Bernoulli random field; Stochastic order; Hardcore lattice gas; 60E15; 60G60; 82B20; 05D40 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-012-0423-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:27:y:2014:i:1:d:10.1007_s10959-012-0423-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-012-0423-6

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().