Inhomogeneous random zero sets

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...

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Authors: Buckley, Jeremiah, Massaneda Clares, Francesc Xavier, Ortega Cerdà, Joaquim
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2014
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/101946
Online Access:https://hdl.handle.net/2445/101946
Access Level:Open access
Keyword:Processos estocàstics
Teoremes de límit (Teoria de probabilitats)
Stochastic processes
Limit theorems (Probability theory)
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spelling Inhomogeneous random zero setsBuckley, JeremiahMassaneda Clares, Francesc XavierOrtega Cerdà, JoaquimProcessos estocàsticsTeoremes de límit (Teoria de probabilitats)Stochastic processesLimit theorems (Probability theory)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.Indiana University2016201620142016info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersion43 p.application/pdfhttps://hdl.handle.net/2445/101946Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió preprint del document publicat a: http://dx.doi.org/10.1512/iumj.2014.63.5260Indiana University Mathematics Journal, 2014, vol. 63, num. 3, p. 739-781http://dx.doi.org/10.1512/iumj.2014.63.5260(c) Indiana University Mathematics Journal, 2014info:eu-repo/semantics/openAccessoai:recercat.cat:2445/1019462026-05-29T05:05:01Z
dc.title.none.fl_str_mv Inhomogeneous random zero sets
title Inhomogeneous random zero sets
spellingShingle Inhomogeneous random zero sets
Buckley, Jeremiah
Processos estocàstics
Teoremes de límit (Teoria de probabilitats)
Stochastic processes
Limit theorems (Probability theory)
title_short Inhomogeneous random zero sets
title_full Inhomogeneous random zero sets
title_fullStr Inhomogeneous random zero sets
title_full_unstemmed Inhomogeneous random zero sets
title_sort Inhomogeneous random zero sets
dc.creator.none.fl_str_mv Buckley, Jeremiah
Massaneda Clares, Francesc Xavier
Ortega Cerdà, Joaquim
author Buckley, Jeremiah
author_facet Buckley, Jeremiah
Massaneda Clares, Francesc Xavier
Ortega Cerdà, Joaquim
author_role author
author2 Massaneda Clares, Francesc Xavier
Ortega Cerdà, Joaquim
author2_role author
author
dc.subject.none.fl_str_mv Processos estocàstics
Teoremes de límit (Teoria de probabilitats)
Stochastic processes
Limit theorems (Probability theory)
topic Processos estocàstics
Teoremes de límit (Teoria de probabilitats)
Stochastic processes
Limit theorems (Probability theory)
description 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.
publishDate 2014
dc.date.none.fl_str_mv 2014
2016
2016
2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/101946
url https://hdl.handle.net/2445/101946
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió preprint del document publicat a: http://dx.doi.org/10.1512/iumj.2014.63.5260
Indiana University Mathematics Journal, 2014, vol. 63, num. 3, p. 739-781
http://dx.doi.org/10.1512/iumj.2014.63.5260
dc.rights.none.fl_str_mv (c) Indiana University Mathematics Journal, 2014
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Indiana University Mathematics Journal, 2014
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 43 p.
application/pdf
dc.publisher.none.fl_str_mv Indiana University
publisher.none.fl_str_mv Indiana University
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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