Maxima of random algebraic curves
Authors:
M. Das and S. S. Bhatt
Journal:
Trans. Amer. Math. Soc. 243 (1978), 195212
MSC:
Primary 60G99
MathSciNet review:
0494482
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Abstract 
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Abstract: Let be a sequence of independent and identically distributed random variables with common characteristic function where , and . Then we show that the numbers of maxima of the curves have expectation , as , where and
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 G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, 1952. MR 0046395 (13:727e)
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 M. Kac, On the average number of real roots of a random algebraic equation, Bull. Amer. Math. Soc. 49 (1943), 314320. MR 0007812 (4:196d)
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 K. Knopp, Theory and application of infinite series, Blackie, London, 1957.
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 B. F. Logan and L. A. Shepp, Real zeros of random polynomials, Proc. London Math. Soc. (3) 18 (1968), 2935. MR 0234512 (38:2829)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719780494482X
PII:
S 00029947(1978)0494482X
Keywords:
Random variables,
distribution,
normally distributed random variables,
sequence,
mathematical expectation,
variance,
characteristic function,
random algebraic curves
Article copyright:
© Copyright 1978
American Mathematical Society
