The speed of a biased random walk on a Galton-Watson tree is analytic
Probability
2020-10-06 v2
Abstract
We prove that the speed of a biased random walk on a supercritical Galton-Watson tree conditioned to survive is analytic within the ballistic regime. This extends the previous work arXiv:1906.07913 in which it was shown that the speed is differentiable within the range of bias for which a central limit theorem holds.
Keywords
Cite
@article{arxiv.2006.03433,
title = {The speed of a biased random walk on a Galton-Watson tree is analytic},
author = {Adam Bowditch and Yuki Tokushige},
journal= {arXiv preprint arXiv:2006.03433},
year = {2020}
}
Comments
Error, the argument of compact convergence is insufficient to prove analyticity for real functions