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The average number of maxima of a random algebraic curve

Published online by Cambridge University Press:  24 October 2008

Minaketan Das
Minaketan Das
Affiliation:
F. M. College, Balasore, India
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Abstract

Let g0, gl, g2,…be a sequence of mutually independent, normally distributed random variables with mathematical expectation zero and variance unity. In this work, we obtain the average number of maxima (minima) of the random algebraic curves with the equations

This average is (½(3½ + 1)) log N + O((log N)⅔ (log log N)½), when N is large.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 741 - 753
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Cramér, H.Random variables and probability distributions, 2nd ed. (Cambridge University Press, 1962).Google Scholar
(2)Cramér, H.Mathematical methods of statistics (Princeton University Press, 1954).Google Scholar
(3)Das, M.The average number of real zeros of a random trigonometric polynomial. Proc. Cambridge Philos. Soc. 64 (1968), 721–729.CrossRefGoogle Scholar
(4)Dunhage, J. E. A.The number of real zeros of a random trigonometric polynomial. Proc. London Math. Soc. (3) 16 (1966), 53–84.CrossRefGoogle Scholar
(5)Erdös, P. and Offord, A. C.On the number of real roots of a random algebraic equation. Proc. London Math. Soc. (3), 6 (1956), 139–160.CrossRefGoogle Scholar
(6)Kac, M.On the average number of real roots of a random algebraic equation. Bull. Amer. Math. Soc. 49 (1943), 314–320.CrossRefGoogle Scholar