Zeros of the i . i . d . Gaussian power series : a conformally invariant determinantal process

@inproceedings{Peres2004ZerosOT,
  title={Zeros of the i . i . d . Gaussian power series : a conformally invariant determinantal process},
  author={Yuval Peres and B{\'a}lint Vir{\'a}g},
  year={2004}
}
Consider the zero set of a random power series ∑ anz n with i.i.d. complex Gaussian coefficients an. We show that these zeros form a determinantal process: more precisely, their joint intensity can be written as a minor of the Bergman kernel. We show that the number of zeros in a disk of radius r about the origin has the same distribution as the sum of independent {0, 1}-valued random variables Xk, where P (Xk = 1) = r2k. The repulsion between zeros can be studied via a dynamic version where… CONTINUE READING
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