English

Local times of subdiffusive biased walks on trees

Probability 2019-01-03 v2

Abstract

Consider a class of null-recurrent randomly biased walks on a super-critical Gaton-Watson tree. We obtain the rates of convergence of the local times and the quenched local probability for the biased walk in the sub-diffusive case. These results are a consequence of a sharp estimate on the return time, whose analysis is driven by a family of concave recursive equations on trees.

Keywords

Cite

@article{arxiv.1412.4507,
  title  = {Local times of subdiffusive biased walks on trees},
  author = {Yueyun Hu},
  journal= {arXiv preprint arXiv:1412.4507},
  year   = {2019}
}

Comments

I am grateful to Pierre Rousselin who has kindly pointed out a mistake in the original version. In this corrected version, the case kappa>2 remains unchanged, but the results in the cases (1 < kappa <= 2) are weaker than that stated in the original version: we only obtain the rates of convergence instead of the exact equivalence with an explicit constant