English

Logarithmic scaling of planar random walk's local times

Probability 2016-03-25 v1

Abstract

We prove that the local time process of a planar simple random walk, when time is scaled logarithmically, converges to a non-degenerate pure jump process. The convergence takes place in the Skorokhod space with respect to the M1M1 topology and fails to hold in the J1J1 topology.

Keywords

Cite

@article{arxiv.1603.07587,
  title  = {Logarithmic scaling of planar random walk's local times},
  author = {Péter Nándori and Zeyu Shen},
  journal= {arXiv preprint arXiv:1603.07587},
  year   = {2016}
}