Universality of Correlations for Random Analytic Functions

Details Universality of Correlations for Random Analytic Functions Universality of Correlations for Random Analytic Functions

2011-07-20

arxiv.org/abs/1107.4135v1

Mathematics

Probability

10 pages, 3 figures. To appear in Contemporary Mathematics, proceedings of the Arizona School of Analysis with Applications, M

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Universality of Correlations for Random Analytic Functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Universality of Correlations for Random Analytic Functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Universality of Correlations for Random Analytic Functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687208