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Synchronization and Functional Central Limit Theorems for Interacting Reinforced Random Walks

Mercredi 11 octobre 10:30-11:30 - Pierre-Yves Louis - Poitiers

Synchronization and Functional Central Limit Theorems for Interacting Reinforced Random Walks

Résumé : 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 algorithms. 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. This is joint work with I. Crimaldi, P. Dai Pra and I. Minelli.

Pour en savoir plus sur cet événement, consultez l'article Séminaires SPOC