BRW pressed against a hard wall

Description

We study bounds on the probability that a branching random walk (BRW) on a ddd-ary tree remains positive at all vertices. Additionally, we examine the expected value at a typical vertex conditioned on the event that the field is positive everywhere. The phenomenon we analyze is that of entropic repulsion in Gaussian fields, which describes the tendency of a field to shift upward when constrained by a hard boundary, such as a positivity condition. Our results show that the conditional expected value at a typical vertex is smaller than the expected maximum of the BRW by a factor of order log⁡n\log nlogn. This finding provides a refinement of existing results on entropic repulsion in Gaussian fields by quantifying the deviation more precisely.

Publication Date

1-1-2017

Keywords

Branching random walk, BRW

Conference

19th January, 2017, ISI Kolkata

This document is currently not available here.

Share

COinS