Large deviations of a random walk model with emerging territories

Abstract

We study an agent-based model of animals marking their territory and evading adversarial territory in one dimension, with respect to the distribution of the size of the resulting territories. In particular, we use sophisticated sampling methods to determine it over a large part of territory sizes, including atypically small and large configurations, which occur with probability of less than $10^{-30}$. We find hints for the validity of a large deviation principle, the shape of the rate function for the right tail of the distribution and insight into the structure of atypical realizations.