relation: http://eprints.imtlucca.it/3031/
title: Fluctuation Theorems for Synchronization of Interacting Polya's urns
creator: Crimaldi, Irene
creator: Dai Pra, Paolo
creator: Minelli, Ida G.
subject: HA Statistics
subject: QA Mathematics
description: 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.
publisher: Elsevier
date: 2016
type: Article
type: PeerReviewed
identifier:   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)  
relation: http://www.sciencedirect.com/science/article/pii/S0304414915002537
relation: 10.1016/j.spa.2015.10.005