eprintid: 3114
rev_number: 7
eprint_status: archive
userid: 36
dir: disk0/00/00/31/14
datestamp: 2016-02-24 12:04:10
lastmod: 2016-02-24 12:04:10
status_changed: 2016-02-24 12:04:10
type: monograph
metadata_visibility: no_search
creators_name: Crimaldi, Irene
creators_name: Dai Pra, Paolo
creators_name: Louis, Pierre-Yves
creators_name: Minelli, Ida G.
creators_id: irene.crimaldi@imtlucca.it
creators_id: daipra@math.unipd.it
creators_id: pierre-yves.louis@math.cnrs.fr
creators_id: ida.minelli@dm.univaq.it
title: Syncronization and functional central limit theorems for interacting reinforced random walks
ispublished: submitted
subjects: HA
subjects: QA
divisions: EIC
full_text_status: none
monograph_type: working_paper
keywords: interacting random systems; synchronization; functional central limit theorems; urn
models; reinforced processes; dynamics on random graphs
note: submitted
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.
date: 2016
date_type: submitted
institution: IMT Institute for Advanced Studies Lucca
official_url: http://arxiv.org/abs/1602.06217
projects: crisis lab
citation:   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)