Monotonicity of escape probabilities for branching random walks on \Z^{d}
Probability
2020-02-28 v2
Abstract
We study nearest-neighbors branching random walks started from a point at the interior of a hypercube. We show that the probability that the process escapes the hypercube is monotonically decreasing with respect to the distance of its starting point from the boundary. We derive as a consequence that at all times the number of particles at a site is monotonically decreasing with respect to its distance from the starting point.
Cite
@article{arxiv.1911.09563,
title = {Monotonicity of escape probabilities for branching random walks on \Z^{d}},
author = {Achillefs Tzioufas},
journal= {arXiv preprint arXiv:1911.09563},
year = {2020}
}
Comments
Added Remark 9