  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.
