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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Oliveira, Roberto I. [1] ; Reis, Guilherme H. [1]
Total Authors: 2
Affiliation:
[1] IMPA, BR-22460320 Rio De Janeiro - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Journal of Statistical Physics; v. 176, n. 5, p. 1057-1087, SEP 2019.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
Grantee:Jefferson Antonio Galves
Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC