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Fluctuation Theorems for Synchronization of Interacting Polya's urns

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)

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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.

Item Type: Article
Identification Number: 10.1016/j.spa.2015.10.005
Additional Information: Available online 23 October 2015
Uncontrolled Keywords: Fluctuation theorem, Interacting system, Stable convergence, Synchronization, Urn model
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Research Area: Economics and Institutional Change
Depositing User: Caterina Tangheroni
Date Deposited: 25 Jan 2016 09:41
Last Modified: 22 Mar 2016 16:00
URI: http://eprints.imtlucca.it/id/eprint/3031

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