A branching random walk in the presence of a hard wall
Document Type
Article
Publication Title
Journal of Applied Probability
Abstract
We consider a branching random walk on a d-ary tree of height n ( n?N ), in the presence of a hard wall which restricts each value to be positive, where d is a natural number satisfying d?2 . We consider the behaviour of Gaussian processes with long-range interactions, for example the discrete Gaussian free field, under the condition that it is positive on a large subset of vertices. We observe a relation with the expected maximum of the processes. We find the probability of the event that the branching random walk is positive at every vertex in the nth generation, and show that the conditional expectation of the Gaussian variable at a typical vertex, under positivity, is less than the expected maximum by order of logn
DOI Link
Publication Date
22-5-2023
Publisher
Cambridge University Press
Volume
Vol.61
Issue
Issu.1
Recommended Citation
Roy, Rishideep, "A branching random walk in the presence of a hard wall" (2023). Faculty Publications. 304.
https://research.iimb.ac.in/fac_pubs/304
