Large deviations of a random walk model with emerging territories
arXiv:2010.00325 · doi:10.1103/PhysRevE.102.062141
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 . 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.
arXiv comment9 pages, 9 figures
References in corpus (13)
- The large deviation approach to statistical mechanics
- Random Convex Hulls and Extreme Value Statistics
- Convex Hull of N Planar Brownian Motions: Exact Results and an Application to Ecology
- Sampling rare events: statistics of local sequence alignments
- Large-deviation properties of the largest biconnected component for random graphs
- Exact distributions of the number of distinct and common sites visited by N independent random walkers
- Convex Hulls of Random Walks: Large-Deviation Properties
- Mean perimeter and mean area of the convex hull over planar random walks
- Large Deviations of Convex Hulls of Self-Avoiding Random Walks
- Convex hull of a Brownian motion in confinement
- Convex Hulls of Random Walks in Higher Dimensions: A Large Deviation Study
- Convex Hulls of Multiple Random Walks: A Large-Deviation Study
- Large Deviations of Convex Hulls of the "True" Self-Avoiding Random Walk