Carregant...
Miniatura

Tipus de document

Article

Versió

Versió enviada

Data de publicació

Tots els drets reservats

Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/101946

Inhomogeneous random zero sets

Títol de la revista

Director/Tutor

ISSN de la revista

Títol del volum

Resum

We construct random point processes in $\C$ that are asymptotically close to a given doubling measure. The processes we construct are the zero sets of random entire functions that are constructed through generalised Fock spaces. We offer two alternative constructions, one via bases for these spaces and another via frames, and we show that for both constructions the average distribution of the zero set is close to the given doubling measure. We prove some asymptotic large deviation estimates for these processes, which in particular allow us to estimate the `hole probability', the probability that there are no zeroes in a given open bounded subset of the plane. We also show that the `smooth linear statistics' are asymptotically normal, under an additional regularity hypothesis on the measure. These generalise previous results by Sodin and Tsirelson for the Lebesgue measure.

Citació

Citació

BUCKLEY, Jeremiah, MASSANEDA CLARES, Francesc xavier, ORTEGA CERDÀ, Joaquim. Inhomogeneous random zero sets. _Indiana University Mathematics Journal_. 2014. Vol. 63, núm. 3, pàgs. 739-781. [consulta: 15 de gener de 2026]. ISSN: 0022-2518. [Disponible a: https://hdl.handle.net/2445/101946]

Exportar metadades

JSON - METS

Compartir registre