The complex zeros of random polynomials
Authors:
Larry A. Shepp and Robert J. Vanderbei
Journal:
Trans. Amer. Math. Soc. 347 (1995), 43654384
MSC:
Primary 30C15; Secondary 60G99
MathSciNet review:
1308023
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Abstract 
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Abstract: Mark Kac gave an explicit formula for the expectation of the number, , of zeros of a random polynomial, in any measurable subset of the reals. Here, are independent standard normal random variables. In fact, for each , he obtained an explicit intensity function for which Here, we extend this formula to obtain an explicit formula for the expected number of zeros in any measurable subset of the complex plane . Namely, we show that where is an explicit intensity function. We also study the asymptotics of showing that for large its mass lies close to, and is uniformly distributed around, the unit circle.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199513080238
PII:
S 00029947(1995)13080238
Article copyright:
© Copyright 1995
American Mathematical Society
