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 walksinteracting 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 coulddirectly apply: urn models and opinion dynamics in a random network evolving via preferential attachment.

Synchronization and functional central limit theorems for interacting reinforced random walks

Crimaldi I;
2019-01-01

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 walksinteracting 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 coulddirectly apply: urn models and opinion dynamics in a random network evolving via preferential attachment.
2019
interacting random systems; synchronization; functional central limit theorems; urn models; reinforced processes; dynamics on random graphs
File in questo prodotto:
File Dimensione Formato  
cri-dai-lou-min-SPA2019-pubblicato.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Nessuna licenza
Dimensione 476.2 kB
Formato Adobe PDF
476.2 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
1602.06217.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 328.09 kB
Formato Adobe PDF
328.09 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/4330
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
social impact