Monotonicity of escape probabilities for branching random walks on \Z^{d}
Abstract
We study nearestneighbors 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.09563
 Bibcode:
 2019arXiv191109563T
 Keywords:

 Mathematics  Probability
 EPrint:
 Added Remark 9