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Random Polynomial

A polynomial having random coefficients.

See also

Kac Formula

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References

Bharucha-Reid, A. T. and Sambandham, M. Random Polynomials. New York: Academic Press, 1986.Bloch, A. and Pólya, G. "On the Zeros of Certain Algebraic Equations." Proc. London Math. Soc. 33, 102-114, 1932.Edelman, A. and Kostlan, E. "How Many Zeros of a Random Polynomial are Real?" Bull. Amer. Math. Soc. 32, 1-37, 1995.Erdős, P. and Turán, P. "On the Distribution of Roots of Polynomials." Ann. Math. 51, 105-119, 1950.Hammersley, J. "The Zeros of a Random Polynomial." Proc. Third Berkeley Symp. Math. Stat. Prob. 2, 89-111, 1956.Kac, M. "On the Average Number of Real Roots of a Random Algebraic Equation." Bull. Amer. Math. Soc. 49, 314-320, 1943.Kac, M. "A Correction to 'On the Average Number of Real Roots of a Random Algebraic Equation.' " Bull. Amer. Math. Soc. 49, 938, 1943.Kostan, E. "On the Distribution of Roots in a Random Polynomial." Ch. 38 in From Topology to Computation: Proceedings of the Smalefest (Ed. M. W. Hirsch, J. E. Marsden, and M. Shub). New York: Springer-Verlag, pp. 419-431, 1993.Littlewood, J. and Offord, A. "On the Number of Real Roots of a Random Algebraic Equation." J. London Math. Soc. 13, 288-295, 1938.Maslova, N. "On the Distribution of the Number of Reals Roots of a Random Polynomial" [In Russian]. Teor. Veroyatnost. i Primenen 19, 488-500, 1974.Rice, S. O. "The Distribution of the Maxima of a Random Curve." Amer. J. Math. 61, 409-416, 1939.Rice, S. O. "Mathematical Analysis of Random Noise." Bell Syst. Tech. J. 24, 45-156, 1945.

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Random Polynomial

Cite this as:

Weisstein, Eric W. "Random Polynomial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RandomPolynomial.html

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