Monotonicity of escape probabilities for branching random walks on \Z^{d}

Achillefs Tzioufas

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arXiv · 1911.09563

Monotonicity of escape probabilities for branching random walks on \Z^{d}

Achillefs Tzioufas

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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.

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Achillefs Tzioufas. 2019-11-21. Monotonicity of escape probabilities for branching random walks on \Z^{d}. https://arxiv.org/abs/1911.09563

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