Differentiability of the speed of biased random walks on Galton-Watson trees

Adam Bowditch, Yuki Tokushige

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We prove that the speed of a λ-biased random walk on a supercritical Galton-Watson tree is differentiable for λ such that the walk is ballistic and obeys a central limit theorem, and give an expression of the derivative using a certain 2-dimensional Gaussian random variable. The proof heavily uses the renewal structure of Galton-Watson trees that was introduced in Lyons et al. (1996).

Original languageEnglish
Pages (from-to)609-642
Number of pages34
JournalAlea (Rio de Janeiro)
Volume17
Issue number1
DOIs
Publication statusPublished - 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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