Tightness for the cover time of the two dimensional sphere

Let C ϵ , S 2 ∗ denote the cover time of the two dimensional sphere by a Wiener sausage of radius ϵ . We prove that C ϵ , S 2 ∗ - 2 A S 2 π log ϵ - 1 - 1 4 log log ϵ - 1 is tight, where A S 2 = 4 π denotes the Riemannian area of S 2 .

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Veröffentlicht in:	Probability theory and related fields 2020-04, Vol.176 (3-4), p.1357-1437
Hauptverfasser:	Belius, David, Rosen, Jay, Zeitouni, Ofer
Format:	Artikel
Sprache:	eng
Schlagworte:	Economics Finance Insurance Management Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Operations Research/Decision Theory Probability Probability Theory and Stochastic Processes Quantitative Finance Statistics for Business Theoretical Tightness
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Beschreibung
Zusammenfassung:	Let C ϵ , S 2 ∗ denote the cover time of the two dimensional sphere by a Wiener sausage of radius ϵ . We prove that C ϵ , S 2 ∗ - 2 A S 2 π log ϵ - 1 - 1 4 log log ϵ - 1 is tight, where A S 2 = 4 π denotes the Riemannian area of S 2 .
ISSN:	0178-8051 1432-2064
DOI:	10.1007/s00440-019-00940-2