Publication

Large deviations for voter model occupation times in two dimensions

Thomas Mountford, Grégory Maillard
2009
Journal Articles

Abstract

We study the decay rate of large deviation probabilities of occupation times, up to time t, for the voter model eta : Z(2) x [0, infinity) -> {0, 1} with simple random walk transition kernel, starting from a Bernoulli product distribution with density rho is an element of (0, 1). In [Probab. Theory Related Fields 77 (1988) 401-413], Bramson, Cox and Griffeath showed that the decay rate order lies in [log(t), log(2)(t)].

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Thomas Mountford, Grégory Maillard
2009
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/c1a8885f-10f5-49a6-ac93-395476d123e1

About this result

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (26)

Large deviations theory

In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While some basic ideas of the theory can be traced to Laplace, the formalization started with insurance mathematics, namely ruin theory with Cramér and Lundberg. A unified formalization of large deviation theory was developed in 1966, in a paper by Varadhan. Large deviations theory formalizes the heuristic ideas of concentration of measures and widely generalizes the notion of convergence of probability measures.

Standard deviation

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Rate function

In mathematics — specifically, in large deviations theory — a rate function is a function used to quantify the probabilities of rare events. Such functions are used to formulate large deviation principle. A large deviation principle quantifies the asymptotic probability of rare events for a sequence of probabilities. A rate function is also called a Cramér function, after the Swedish probabilist Harald Cramér. Rate function An extended real-valued function I : X → [0, +∞] defined on a Hausdorff topological space X is said to be a rate function if it is not identically +∞ and is lower semi-continuous, i.

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