TY  - RPRT
KW  - interacting random systems; synchronization; functional central limit theorems; urn
models; reinforced processes; dynamics on random graphs
N2  - We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are correlated, forcing their convergence to the same, possibly random, limit. Random walks of this form have been introduced in the context of urn models and in stochastic approximation. We also propose an application to opinion dynamics in a random network evolving via preferential attachment. We study, in particular, random walks interacting through a mean-field rule and compare the rate they converge to their limit with the rate of synchronization, i.e. the rate at which their mutual distances converge to zero. Under certain conditions, synchronization is faster than convergence.
N1  - submitted
UR  - http://arxiv.org/abs/1602.06217
TI  - Syncronization and functional central limit theorems for interacting reinforced random walks
ID  - eprints3114
M1  - working_paper
AV  - none
A1  - Crimaldi, Irene
A1  - Dai Pra, Paolo
A1  - Louis, Pierre-Yves
A1  - Minelli, Ida G.
Y1  - 2016///
ER  -