Large deviations of a random walk model with emerging territories

TL;DR

This paper investigates the probability of rare large deviations in a one-dimensional animal territory model, revealing insights into the distribution's tail behavior and the structure of unlikely territory configurations.

Contribution

It introduces advanced sampling techniques to analyze extremely rare events in a territorial model, providing evidence for a large deviation principle and characterizing the rate function.

Findings

Hints for a large deviation principle in the model

Shape of the rate function for large territories

Insights into the structure of atypical territory configurations

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.