# Universality for zeros of random analytic functions

@article{Kabluchko2012UniversalityFZ, title={Universality for zeros of random analytic functions}, author={Zakhar Kabluchko and Dmitry Zaporozhets}, journal={arXiv: Probability}, year={2012} }

Let 0; 1;::: be independent identically distributed (i.i.d.) ran- dom variables such that E log(1 +j 0j) < 1. We consider random analytic functions of the form Gn(z) = 1 X k=0 kfk;nz k ; n logf(tn);n! u(t) as n!1, where u(t) is some function, we show that the measure n converges weakly to some deterministic measure which is characterized in terms of the Legendre{Fenchel transform of u. The limiting measure is universal, that is it does not depend on the distribution of the k's. This result is…

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