An LIL for cover times of disks by planar random walk and Wiener sausage

Details An LIL for cover times of disks by planar random walk and Wiener sausage An LIL for cover times of disks by planar random walk and Wiener sausage

2004-09-15

arxiv.org/abs/math/0409239v2

Mathematics

Probability

18 pages to appear, Trans. Amer. Math. Soc

Scientific paper

Let R_n be the radius of the largest disk covered after n steps of a simple
random walk. We prove that almost surely limsup_{n \to \infty}(log R_n)^2/(log
n log_3 n) = 1/4, where log_3 denotes 3 iterations of the log function. This is
motivated by a question of Erd\H{o}s and Taylor. We also obtain the analogous
result for the Wiener sausage, refining a result of Meyre and Werner.

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