The subleading order of two dimensional cover times
type: Item
instance of: scholarly article
title: The subleading order of two dimensional cover times
zbMATH Open document ID: 1365.60071
author: David Belius
author: Nicola Kistler
publication date: 2017-02-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1405.0888
review text: The \(\varepsilon \)-cover time of the two-dimensional torus by Brownian motion is the time it takes for the process to come within distance \(\varepsilon > 0\) from any point. \textit{A. Dembo} et al. [Ann. Math. (2) 160, No. 2, 433--464 (2004; Zbl 1068.60018)] proved the law of large numbers: \(\frac{{{C_\varepsilon }}}{{\frac{1}{\pi }\log {\varepsilon ^{ - 1}}}} = (1 + o(1))\log{\varepsilon ^{ - 2}}\), \(\varepsilon \to 0\). The authors improve this result: \(\frac{{{C_\varepsilon }}}{{\frac{1}{\pi }\log {\varepsilon ^{ - 1}}}} = \log {\varepsilon ^{ - 2}} - (1 + o(1))\log\log{\varepsilon ^{ - 1}}\) in probability, as \(\varepsilon \to 0\).
reviewed by: Oleg K. Zakusilo
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 6685608
zbMATH Keywords: Brownian motion
zbMATH Keywords: torus
zbMATH Keywords: cover times
zbMATH Keywords: extremes
zbMATH Keywords: branching Brownian motion
zbMATH Keywords: second moment method
MaRDI profile type: Publication
OpenAlex ID: W2257118316
arXiv ID: 1405.0888
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DOI: 10.1007/S00440-015-0689-6
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article