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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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An LIL for cover times of disks by planar random walk and Wiener sausage
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by J. Ben Hough and Yuval Peres PDF
Trans. Amer. Math. Soc. 359 (2007), 4653-4668

Abstract:

Let $R_n$ be the radius of the largest disk covered after $n$ steps of a simple random walk. We prove that almost surely \[ \limsup _{n \rightarrow \infty }(\log R_n)^2/(\log n \log _3 n) = 1/4,\] where $\log _3$ denotes 3 iterations of the $\log$ function. This is motivated by a question of Erdős and Taylor. We also obtain the analogous result for the Wiener sausage, refining a result of Meyre and Werner.
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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
  • MR Author ID: 137920
  • Email: peres@stat.berkeley.edu
  • Received by editor(s): September 18, 2004
  • Received by editor(s) in revised form: January 5, 2005
  • Published electronically: May 1, 2007
  • Additional Notes: The authors gratefully acknowledge the financial support from NSF grants $\#$DMS-0104073 and $\#$DMS-0244479
  • © Copyright 2007 by J. Ben Hough and Yuval Peres
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 4653-4668
  • MSC (2000): Primary 60F15
  • DOI: https://doi.org/10.1090/S0002-9947-07-03966-9
  • MathSciNet review: 2320645