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An LIL for cover times of disks by planar random walk and Wiener sausage
Author(s):
J.
Ben
Hough;
Yuval
Peres
Journal:
Trans. Amer. Math. Soc.
359
(2007),
4653-4668.
MSC (2000):
Primary 60F15
Posted:
May 1, 2007
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Abstract:
Let  be the radius of the largest disk covered after  steps of a simple random walk. We prove that almost surely where  denotes 3 iterations of the  function. This is motivated by a question of Erdos and Taylor. We also obtain the analogous result for the Wiener sausage, refining a result of Meyre and Werner.
References:
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Additional Information:
J.
Ben
Hough
Affiliation:
Department of Mathematics, University of California Berkeley, Berkeley, California 94720
Address at time of publication:
HBK Capital Management, 350 Park Avenue, Fl 20, New York, New York 10022
Email:
jbhough@math.berkeley.edu
Yuval
Peres
Affiliation:
Departments of Statistics and Mathematics, University of California Berkeley, Berkeley, California 94720
Email:
peres@stat.berkeley.edu
DOI:
10.1090/S0002-9947-07-03966-9
PII:
S 0002-9947(07)03966-9
Received by editor(s):
September 18, 2004
Received by editor(s) in revised form:
January 5, 2005
Posted:
May 1, 2007
Additional Notes:
The authors gratefully acknowledge the financial support from NSF grants $\#$DMS-0104073 and $\#$DMS-0244479
Copyright of article:
Copyright
2007,
by J. Ben Hough and Yuval Peres
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