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http://hdl.handle.net/2445/192549
Title: | Volume fluctuations of random analytic varieties in the unit ball |
Author: | Massaneda Clares, Francesc Xavier Pridhnani, Bharti |
Keywords: | Espais analítics Processos gaussians Analytic spaces Gaussian processes |
Issue Date: | 23-Nov-2015 |
Publisher: | Indiana University |
Abstract: | Given a Gaussian analytic function $f_L$ of intesity $L$ in the unit ball of $\mathbb{C}^n, n \geq 2$, consider its (random) zero variety $Z\left(f_L\right)$. We reduce the variance of the $(n-1)$-dimensional volume of $Z\left(f_L\right)$ inside a pseudo-hyperbolic ball of radius $r$ to an integral of a positive function in the unit disk. We illustrate the usefulness of this expression by describing the asymptotic behaviour of the variance as $r \rightarrow 1^{-}$and as $L \rightarrow \infty$. Both the results and the proofs generalise to the ball those given by Jeremiah Buckley for the unit disk. |
Note: | Versió preprint del document publicat a: https://www.jstor.org/stable/26316201 |
It is part of: | Indiana University Mathematics Journal, 2015, vol. 64, num. 6, p. 1667-1695 |
URI: | http://hdl.handle.net/2445/192549 |
ISSN: | 0022-2518 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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644426.pdf | 226.49 kB | Adobe PDF | View/Open |
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