eprintid: 3031
rev_number: 7
eprint_status: archive
userid: 69
dir: disk0/00/00/30/31
datestamp: 2016-01-25 09:41:37
lastmod: 2016-03-22 16:00:42
status_changed: 2016-01-25 09:41:37
type: article
succeeds: 2262
metadata_visibility: show
creators_name: Crimaldi, Irene
creators_name: Dai Pra, Paolo
creators_name: Minelli, Ida G.
creators_id: irene.crimaldi@imtlucca.it
creators_id: daipra@math.unipd.it
creators_id: ida.minelli@dm.univaq.it
title: Fluctuation Theorems for Synchronization of Interacting Polya's urns
ispublished: pub
subjects: HA
subjects: QA
divisions: EIC
full_text_status: none
monograph_type: technical_report
keywords: Fluctuation theorem, Interacting system, Stable convergence, Synchronization, Urn model
note: Available online 23 October 2015
abstract: We consider a model of N two-colors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of mean-field type and it is tuned by a parameter \alpha in [0,1]; in particular, for \alpha=0 the N urns behave as N independent Polya's urns. For \alpha>0 urns synchronize, in the sense that the fraction of balls of a given color converges a.s. to the same (random) limit in all urns. In this paper we study fluctuations around this synchronized regime. The scaling of these fluctuations depends on the parameter \alpha. In particular, the standard scaling t^{-1/2} appears only for \alpha>1/2. For \alpha\geq 1/2 we also determine the limit distribution of the rescaled fluctuations. We use the notion of stable convergence, which is stronger than convergence in distribution.
date: 2016
date_type: published
publication: Stochastic processes and their applications
volume: 126
number: 3
publisher: Elsevier
pagerange: 930-947
pages: 15
id_number: 10.1016/j.spa.2015.10.005
institution: IMT Institute for Advanced Studies Lucca
refereed: TRUE
issn: 0304-4149
official_url: http://www.sciencedirect.com/science/article/pii/S0304414915002537
citation:   Crimaldi, Irene and Dai Pra, Paolo and Minelli, Ida G.  Fluctuation Theorems for Synchronization of Interacting Polya's urns.  Stochastic processes and their applications, 126 (3).  pp. 930-947.  ISSN 0304-4149      (2016)