TY  - RPRT
KW  - Fluctuation theorem
KW  -  Interacting system
KW  -  Stable convergence
KW  -  Synchronization
KW  -  Urn model
N2  - 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. 
N1  - preprint on ArXiv (1407.5043), submitted 
UR  - http://arxiv-web3.library.cornell.edu/abs/1407.5043?context=math
TI  - Fluctuation Theorems for Synchronization of Interacting Polya's urns
ID  - eprints2262
M1  - technical_report
AV  - none
A1  - Crimaldi, Irene
A1  - Dai Pra, Paolo
A1  - Minelli, Ida G.
Y1  - 2014/07//
EP  - 15
ER  -