Critical points of random polynomials with independent identically distributed roots. (English) Zbl 1314.30008
This paper deals with stochastic polynomials, whose roots are independent and identically distributed in the complex plane. The author studies the relationship between the distribution of the roots of a stochastic polynomial and the distribution of its critical points (in other words the roots of the derivative of this polynomial). It is proved that a probability measure, which assigns to each critical point of the polynomial the same weight (the empirical measure), converges in probability to the distribution of the roots of the polynomial.
Reviewer: Anatoliy Pogorui (Zhytomyr)
MSC:
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
| 60G57 | Random measures |
| 60B10 | Convergence of probability measures |
Keywords:
random polynomials; empirical distribution; critical points; zeros of the derivative; logarithmic potentialReferences:
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