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Seminari di Fisica Matematica Dipartimento di Matematica "G. Castelnuovo" Università di Roma La Sapienza

Mercoledì 28 settembre, ore 16, aula di Consiglio

Giambattista Giacomin (Université Paris Diderot)

Dynamical models on random graphs: mean field versus long time behavior

Abstract. I will address the issue of the proximity of interacting diffusion models on large graphs with a uniform degree property and the corresponding mean field model, i.e. a model on the complete graph with a suitably renormalized interaction parameter. Examples include Erdos-Renyi graphs with edge probability p(n), n is the number of vertices, such that p(n)n tends to infinity as n does. I will present a general result establishing this proximity on finite time horizon, by exploiting the fact that both systems are accurately described by a Fokker-Planck PDE in the limit. I will then try to put this result into perspective by discussing the limitations of our approach.

Tutti gli interessati sono invitati a partecipare.

---------------------------------------------------------------- Gustavo Posta

Dipartimento di Matematica Università di Roma "la Sapienza" P.le A. Moro 2, 00185 Roma Italy

web: http://www1.mat.uniroma1.it/~posta e-mail: gustavo.posta@uniroma1.it phone: +39-06-4991-4969 ------------------------------------------------------------------