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