On the range of the transient frog model on Z
Probability
2015-02-11 v1
Abstract
In this paper we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for the moments of the lower bound of the model's long-run range, as well as their asymptotic limits as the drift of the underlying random walk vanishes. We also provide conditions in which the lower bound can be scaled to converge in probability to the degenerate distribution at 1 as the drift vanishes.
Keywords
Cite
@article{arxiv.1502.02738,
title = {On the range of the transient frog model on Z},
author = {Arka P. Ghosh and Steven Noren and Alexander Roitershtein},
journal= {arXiv preprint arXiv:1502.02738},
year = {2015}
}