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. 930947. ISSN 03044149 (2016)
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Abstract
We consider a model of N twocolors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of meanfield 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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Fluctuation Theorems for Synchronization of Interacting Polya's urns. (deposited 23 Jul 2014 09:02)
 Fluctuation Theorems for Synchronization of Interacting Polya's urns. (deposited 25 Jan 2016 09:41) [Currently Displayed]
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