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Complex Roots of a Random Algebraic Polynomial

✍ Scribed by K. Farahmand

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
160 KB
Volume
210
Category
Article
ISSN
0022-247X

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✦ Synopsis

This paper, for any constant K, provides an exact formula for the average density of the distribution of the complex roots of equation q z q z 2 0 1 2 n y 1 Γ„ 4 ny1 Γ„ 4 ny1 qΠΈΠΈΠΈ q z s K where s a q ib and a and b are sequences

of independent identically and normally distributed random variables and K is a complex number with K as its real and imaginary parts. The case of real roots of the above equation with real coefficients and K, z g R is well known. Further we obtain the limiting behaviour of this distribution function as n tends to infinity.

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