Synchronization and functional central limit theorems for interacting reinforced random walks

Irene Crimaldi, Paolo Dai Pra, Pierre-Yves Louis and Ida G. Minelli

Stochastic Processes and their Applications, 2019, vol. 129, issue 1, 70-101

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.

Keywords: Interacting random systems; Synchronization; Functional central limit theorems; Urn models; Reinforced processes; Dynamics on random graphs (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:1:p:70-101

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DOI: 10.1016/j.spa.2018.02.012

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