eprintid: 2262
rev_number: 13
eprint_status: archive
userid: 36
dir: disk0/00/00/22/62
datestamp: 2014-07-23 09:02:18
lastmod: 2014-07-23 09:02:18
status_changed: 2014-07-23 09:02:18
type: monograph
metadata_visibility: no_search
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: submitted
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: preprint on ArXiv (1407.5043), submitted 
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: 2014-07
pages: 15
institution: IMT Institute for Advanced Studies Lucca
official_url: http://arxiv-web3.library.cornell.edu/abs/1407.5043?context=math
citation:   Crimaldi, Irene and Dai Pra, Paolo and Minelli, Ida G.  Fluctuation Theorems for Synchronization of Interacting Polya's urns.  Technical Report       (Submitted)