Tightness for the Cover Time of the two dimensional sphere

David Belius; Jay Rosen; Ofer Zeitouni

Tightness for the Cover Time of the two dimensional sphere

Probability 2020-02-10 v6

Authors: David Belius , Jay Rosen , Ofer Zeitouni

Abstract

Let $C^*_{\epsilon,S^2}$ denote the cover time of the two dimensional sphere by a Wiener sausage of radius $\epsilon$ . We prove that $\sqrt{C^{*}_{\epsilon,S^2} } -\sqrt{\frac{2A_{S^2}}{\pi}}(\log \epsilon^{-1}-\frac14\log\log \epsilon^{-1})$ is tight, where $A_{S^2}=4\pi$ denotes the Riemannian area of $S^2$ .

Keywords

cover time wiener sausage two dimensional sphere tightness riemannian area

Cite

@article{arxiv.1711.02845,
  title  = {Tightness for the Cover Time of the two dimensional sphere},
  author = {David Belius and Jay Rosen and Ofer Zeitouni},
  journal= {arXiv preprint arXiv:1711.02845},
  year   = {2020}
}

Comments

Third version deals only with the sphere, because the reduction from general manifold to the sphere in the second version contains a mistake. V5 corrects an error in the statement of Lemma 9.1, and its use in the first and second moment estimates (replacing the former erroneous estimates (4.56) and (4.87)). V6 corrects minor typos, and added details to the statement and proof of Lemma 9.2

Tightness for the Cover Time of the two dimensional sphere

Abstract

Keywords

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