Correlation functions for zeros of a Gaussian power series and Pfaffians

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.

arXiv comment22 pages, the final version

References in corpus (5)

• Eigenvalue statistics of the real Ginibre ensemble
• The Ginibre ensemble of real random matrices and its scaling limits
• Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process
• Pfaffian formulae for one dimensional coalescing and annihilating systems
• The limiting Kac random polynomial and truncated random orthogonal matrices

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