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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Multiple points of transient random walks
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by Joel H. Pitt PDF
Proc. Amer. Math. Soc. 43 (1974), 195-199 Request permission


We determine the asymptotic behavior of the expected numbers of points visited exactly $j$ times and at least $j$ times in the first $n$ steps of a transient random walk on a discrete Abelian group. We prove that the strong law of large numbers holds for these multiple point ranges.
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  • P. Erdős and S. J. Taylor, Some problems concerning the structure of random walk paths, Acta Math. Acad. Sci. Hungar. 11 (1960), 137–162. (unbound insert) (English, with Russian summary). MR 121870, DOI 10.1007/BF02020631
  • Frank Spitzer, Principles of random walk, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1964. MR 0171290
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 195-199
  • MSC: Primary 60J15
  • DOI:
  • MathSciNet review: 0386021