Correlations between zeros of a random polynomial

Details Correlations between zeros of a random polynomial Correlations between zeros of a random polynomial

2002-01-04

arxiv.org/abs/math-ph/0201012v2

Journ. Statist. Phys. 88 (1997), 269-305

Physics

Mathematical Physics

31 pages, 2 figures; a revised version of the J. Stat. Phys. paper

Scientific paper

We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval $(-1,1)$ are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random polynomial.

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