Two sufficient conditions for Poisson approximations in the ferromagnetic Ising model

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dc.creatorCoupier, David
dc.date2006-10-30
dc.date2008-08-26
dc.date.accessioned2026-07-07T09:58:47Z
dc.date.available2026-07-07T09:58:47Z
dc.descriptionA $d$-dimensional ferromagnetic Ising model on a lattice torus is considered. As the size of the lattice tends to infinity, two conditions ensuring a Poisson approximation for the distribution of the number of occurrences in the lattice of any given local configuration are suggested. The proof builds on the Stein--Chen method. The rate of the Poisson approximation and the speed of convergence to it are defined and make sense for the model. Thus, the two sufficient conditions are traduced in terms of the magnetic field and the pair potential. In particular, the Poisson approximation holds even if both potentials diverge.
dc.descriptionPublished in at http://dx.doi.org/10.1214/1214/07-AAP487 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0610939
dc.identifierhttp://arxiv.org/abs/math/0610939
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 4, 1326-1350
dc.identifierdoi:10.1214/1214/07-AAP487
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167843
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60F05 (Primary) 82B20 (Secondary)
dc.titleTwo sufficient conditions for Poisson approximations in the ferromagnetic Ising model
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