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作者：Coupier, David
作者单位：Universite de Lille
摘要：A 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...
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作者：Windisch, David
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a random walk on the discrete cylinder (7G/NZ)d x 7G, d >_ 3 with drift N-d,, in the 7G-direction and investigate the large N-behavior of the disconnection time TNts, defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent a is strictly greater than 1, the asymptotic behavior of TNts remains NZd+o(1) as in the unbiased case considered by Dembo and Sznitman, whereas for a < 1...
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作者：Eichelsbacher, Peter; Reinert, Gesine
作者单位：Ruhr University Bochum; University of Oxford
摘要：Stein's method provides a way of bounding the distance of a probability distribution to a target distribution jL. Here we develop Stein's method for the class of discrete Gibbs measures with a density ev, where V is the energy function. Using size bias couplings, we treat an example of Gibbs convergence for strongly correlated random variables due to Chayes and Klein [Helv. Phys. Acta 67 (1994) 30-42]. We obtain estimates of the approximation to a grand-canonical Gibbs ensemble. As side result...
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作者：Herrmann, Samuel; Imkeller, Peter; Peithmann, Dierk
作者单位：Universite de Lorraine; Humboldt University of Berlin
摘要：We investigate exit times from domains of attraction for the motion of a self-stabilized particle traveling in a geometric (potential type) landscape and perturbed by Brownian noise of small amplitude. Self-stabilization is the effect of including an ensemble-average attraction in addition to the usual state-dependent drift, where the particle is supposed to be suspended in a large population of identical ones. A Kramers' type law for the particle's exit from the potential's domains of attract...
