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Article overview
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Universality of Correlations for Random Analytic Functions | Shannon Starr
; | Date: |
21 Jul 2011 | Abstract: | We review a result obtained with Andrew Ledoan and Marco Merkli. Consider a
random analytic function $f(z) = sum_{n=0}^{infty} a_n X_n z^n$, where the
$X_n$’s are i.i.d., complex valued random variables with mean zero and unit
variance, and the coefficients $a_n$ are non-random and chosen so that the
variance transforms covariantly under conformal transformations of the domain.
If the $X_n$’s are Gaussian, this is called a Gaussian analytic function (GAF).
We prove that, even if the coefficients are not Gaussian, the zero set
converges in distribution to that of a GAF near the boundary of the domain. | Source: | arXiv, 1107.4135 | Services: | Forum | Review | PDF | Favorites |
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