Monotonicity of escape probabilities for branching random walks on \Z^{d}
arXiv:1911.09563
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.
Added Remark 9