二维球面覆盖时间的紧性

David Belius; Jay Rosen; Ofer Zeitouni

二维球面覆盖时间的紧性

概率论 2020-02-10 v6

作者: David Belius , Jay Rosen , Ofer Zeitouni

摘要

令 $C^*_{\epsilon,S^2}$ 表示半径为 $\epsilon$ 的维纳香肠对二维球面的覆盖时间。我们证明 $\sqrt{C^{*}_{\epsilon,S^2} } -\sqrt{\frac{2A_{S^2}}{\pi}}(\log \epsilon^{-1}-\frac14\log\log \epsilon^{-1})$ 是紧的，其中 $A_{S^2}=4\pi$ 表示 $S^2$ 的黎曼面积。

关键词

覆盖时间维纳香肠二维球面紧性黎曼面积

引用

@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}
}

备注

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

二维球面覆盖时间的紧性

摘要

关键词

引用

备注

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