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

Richard S. Ellis & Shlomo Ta’asan

International Journal of Stochastic Analysis2015https://doi.org/10.1155/2015/287450article
ABDC B
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0.26

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 b∈N and c>b, K distinguishable particles are placed, each with equal probability 1/N, onto the N sites of a lattice, where K/N equals c. We focus on configurations for which each site is occupied by a minimum of b particles. The main result is the large deviation principle (LDP), in the limit K→∞ and N→∞ with K/N=c, 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 R(θ∣ρ∗), where θ is a possible asymptotic configuration of the number-density measures and ρ∗ is a Poisson distribution with mean c, restricted to the set of positive integers n satisfying n≥b. This LDP implies that ρ∗ is the equilibrium distribution of the number-density measures, which in turn implies that ρ∗ is the equilibrium distribution of the random variables that count the droplet sizes.

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https://doi.org/https://doi.org/10.1155/2015/287450

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@article{richard2015,
  title        = {{Large Deviation Analysis of a Droplet Model Having a Poisson Equilibrium Distribution}},
  author       = {Richard S. Ellis & Shlomo Ta’asan},
  journal      = {International Journal of Stochastic Analysis},
  year         = {2015},
  doi          = {https://doi.org/https://doi.org/10.1155/2015/287450},
}

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0.26

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.00 × 0.4 = 0.00
M · momentum0.20 × 0.15 = 0.03
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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