TY  - JOUR
SN  - 0304-4149
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.
KW  - Fluctuation theorem
KW  -  Interacting system
KW  -  Stable convergence
KW  -  Synchronization
KW  -  Urn model
AV  - none
TI  - Fluctuation Theorems for Synchronization of Interacting Polya's urns
UR  - http://www.sciencedirect.com/science/article/pii/S0304414915002537
ID  - eprints3031
N1  - Available online 23 October 2015
EP  - 947
PB  - Elsevier
A1  - Crimaldi, Irene
A1  - Dai Pra, Paolo
A1  - Minelli, Ida G.
SP  - 930
Y1  - 2016///
JF  - Stochastic processes and their applications
IS  - 3
VL  - 126
ER  -