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Syncronization and functional central limit theorems for interacting reinforced random walks

Crimaldi, Irene and Dai Pra, Paolo and Louis, Pierre-Yves and Minelli, Ida G. Syncronization and functional central limit theorems for interacting reinforced random walks. Working Paper (Submitted)

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Abstract

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.

Item Type: Working Paper (Working Paper)
Additional Information: submitted
Projects: crisis lab
Uncontrolled Keywords: interacting random systems; synchronization; functional central limit theorems; urn models; reinforced processes; dynamics on random graphs
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Research Area: Economics and Institutional Change
Depositing User: Irene Crimaldi
Date Deposited: 24 Feb 2016 12:04
Last Modified: 24 Feb 2016 12:04
URI: http://eprints.imtlucca.it/id/eprint/3114

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