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arXiv · 1711.02845

Tightness for the Cover Time of the two dimensional sphere

David Belius·Jay Rosen·Ofer Zeitouni
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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 $S^2$.

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David Belius, Jay Rosen, Ofer Zeitouni. 2017-11-08. Tightness for the Cover Time of the two dimensional sphere. https://arxiv.org/abs/1711.02845

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