eprintid: 3942
rev_number: 5
eprint_status: archive
userid: 36
dir: disk0/00/00/39/42
datestamp: 2018-03-05 09:56:48
lastmod: 2018-03-05 09:56:48
status_changed: 2018-03-05 09:56:48
type: article
succeeds: 3114
metadata_visibility: show
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: Synchronization and functional central limit theorems for interacting reinforced random walks
ispublished: inpress
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
abstract: We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks. Due to a reinforcement mechanism and interaction, the walks are strongly correlated and converge almost surely to the same, possibly random, limit. We study 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. We show that, under certain conditions, synchronization is faster than convergence. Even if our focus is on theoretical results, we propose as main motivations two contexts in which such results could directly apply: urn models and opinion dynamics in a random network evolving via preferential attachment.
date_type: published
publication: Stochastic processes and their applications
publisher: Elsevier
institution: IMT Institute for Advanced Studies Lucca
refereed: TRUE
issn: 0304-4149
projects: crisis lab
citation:   Crimaldi, Irene and Dai Pra, Paolo and Louis, Pierre-Yves and Minelli, Ida G.  Synchronization and functional central limit theorems for interacting reinforced random walks.  Stochastic processes and their applications.   ISSN 0304-4149    (In Press)