2026-04-14T04:39:01Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/1019462025-12-05T09:56:28Zcom_2072_1057col_2072_478917col_2072_478920

00925njm 22002777a 4500 dc Buckley, Jeremiah author Massaneda Clares, Francesc Xavier author Ortega Cerdà, Joaquim author 2016-09-20T11:27:37Z 2016-09-20T11:27:37Z 2014 2016-09-20T11:27:42Z 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. Processos estocàstics Teoremes de límit (Teoria de probabilitats) Stochastic processes Limit theorems (Probability theory) Inhomogeneous random zero sets