Monotonicity of escape probabilities for branching random walks on \Z^{d}
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.09563
- arXiv:
- arXiv:1911.09563
- Bibcode:
- 2019arXiv191109563T
- Keywords:
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- Mathematics - Probability
- E-Print:
- Added Remark 9