Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Files

644426.pdf (226.49 KB)

Document type

Article

Version

Submitted version

Publication date

2015-11-23

All rights reserved

Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/192549

Volume fluctuations of random analytic varieties in the unit ball

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

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.

Subject

Espais analítics, Processos gaussians

Subject (English)

Analytic spaces, Gaussian processes

Citation

Collections

Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

MASSANEDA CLARES, Francesc Xavier and PRIDHNANI, Bharti. Volume fluctuations of random analytic varieties in the unit ball. Indiana University Mathematics Journal. 2015. Vol. 64, num. 6, pags. 1667-1695. ISSN 0022-2518. [consulted: 10 of August of 2026]. Available at: https://hdl.handle.net/2445/192549

Export metadata

JSON - METS

Share record