English

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