Correlation functions for zeros of a Gaussian power series and Pfaffians

2012/12/31 by Sho Matsumoto, Tomoyuki Shirai · 1 citation
Mathematics · #math.PR

paper · pdf · doi:10.1214/ejp.v18-2545

published as Electronic Journal of Probability 18 (2013), no. 49, 1--18 · 22 pages, the final version

arxiv created 2013/04/16 · arxiv updated 2013/04/17

Abstract

We show that the zeros of the random power series with i.i.d. real Gaussian coefficients form a Pfaffian point process. We further show that the product moments for absolute values and signatures of the power series can also be expressed by Pfaffians.

Cited by

• Gaussian limit for Pfaffian point processes