[PDF][PDF] Limit theorems for random analytic functions and their zeros: dedicated to the late professor Yasunori Okabe (functions in number theory and their probabilistic …
T Shirai - 数理解析研究所講究録別冊, 2012 - repository.kulib.kyoto-u.ac.jp
数理解析研究所講究録別冊, 2012•repository.kulib.kyoto-u.ac.jp
After we briefly review on determinantal point processes and Gaussian analytic functions,
we establish a functional central limit theorem for random analytic functions and the corre‐
sponding limit theorem for their zero processes. We also show that the zeros of the complex
Wiener integral of the Szegö kernel for the upper half‐plane form a determinantal point
process on it.
we establish a functional central limit theorem for random analytic functions and the corre‐
sponding limit theorem for their zero processes. We also show that the zeros of the complex
Wiener integral of the Szegö kernel for the upper half‐plane form a determinantal point
process on it.
Abstract
After we briefly review on determinantal point processes and Gaussian analytic functions, we establish a functional central limit theorem for random analytic functions and the corre‐sponding limit theorem for their zero processes. We also show that the zeros of the complex Wiener integral of the Szegö kernel for the upper half‐plane form a determinantal point process on it.
repository.kulib.kyoto-u.ac.jp
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