Interacting Diffusions on Random Graphs with Diverging Average Degrees: Hydrodynamics and Large Deviations

Autor(es)

Oliveira, Roberto I. ^[1] ; Reis, Guilherme H. ^[1]

Afiliação do(s) autor(es)

^[1] IMPA, BR-22460320 Rio De Janeiro - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 176, n. 5, p. 1057-1087, SEP 2019.
• Citações Web of Science: 0

Resumo

We consider systems of mean-field interacting diffusions, where the pairwise interaction structure is described by a sparse (and potentially inhomogeneous) random graph. Examples include the stochastic Kuramoto model with pairwise interactions given by an Erdos-Renyi graph. Our problem is to compare the bulk behavior of such systems with that of corresponding systems with dense nonrandom interactions. For a broad class of interaction functions, we find the optimal sparsity condition that implies that the two systems have the same hydrodynamic limit, which is given by a McKean-Vlasov diffusion. Moreover, we also prove matching behavior of the two systems at the level of large deviations. Our results extend classical results of dai Pra and den Hollander and provide the first examples of LDPs for systems with sparse random interactions. (AU)

• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Oswaldo Baffa Filho
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs