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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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Level crossings of a random polynomial with hyperbolic elements
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by K. Farahmand PDF
Proc. Amer. Math. Soc. 123 (1995), 1887-1892 Request permission

Abstract:

This paper provides an asymptotic estimate for the expected number of K-level crossings of a random hyperbolic polynomial ${g_1}\cosh x + {g_2}\cosh 2x + \cdots + {g_n}\cosh nx$, where ${g_j}(j = 1,2, \ldots ,n)$ are independent normally distributed random variables with mean zero, variance one and K is any constant independent of x. It is shown that the result for $K = 0$ remains valid as long as $K \equiv {K_n} = O(\sqrt n )$.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1887-1892
  • MSC: Primary 60H99; Secondary 42A05
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1264810-1
  • MathSciNet review: 1264810