Large Deviation Analysis of a Droplet Model Having a Poisson Equilibrium Distribution

Richard S. Ellis and Shlomo Ta’asan

International Journal of Stochastic Analysis, 2015, vol. 2015, 1-15

Abstract:

In this paper we use large deviation theory to determine the equilibrium distribution of a basic droplet model that underlies a number of important models in material science and statistical mechanics. Given and , distinguishable particles are placed, each with equal probability , onto the sites of a lattice, where equals . We focus on configurations for which each site is occupied by a minimum of particles. The main result is the large deviation principle (LDP), in the limit and with , for a sequence of random, number-density measures, which are the empirical measures of dependent random variables that count the droplet sizes. The rate function in the LDP is the relative entropy , where is a possible asymptotic configuration of the number-density measures and is a Poisson distribution with mean , restricted to the set of positive integers satisfying . This LDP implies that is the equilibrium distribution of the number-density measures, which in turn implies that is the equilibrium distribution of the random variables that count the droplet sizes.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:287450

DOI: 10.1155/2015/287450

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