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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Representation of $0$ as $\sum ^{N}_{K=-N} \varepsilon _{k}k$
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by J. H. van Lint
Proc. Amer. Math. Soc. 18 (1967), 182-184
DOI: https://doi.org/10.1090/S0002-9939-1967-0205964-8
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Abstract:

If ${\varepsilon _k}$ are independent identically distributed random variables with values $0$ and $1$, each with probability $\tfrac {1} {2}$ then \[ P\left ( {\sum \limits _{k = - N}^{ + N} {{\varepsilon _k}k = 0} } \right ) \sim {\left ( {\frac {3} {\pi }} \right )^{1/2}}{N^{ - 3/2}}.\]
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Bibliographic Information
  • © Copyright 1967 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 18 (1967), 182-184
  • MSC: Primary 10.25
  • DOI: https://doi.org/10.1090/S0002-9939-1967-0205964-8
  • MathSciNet review: 0205964