Interacting diffusions on sparse graphs: hydrodynamics from local weak limits

Autor(es)

Oliveira, I, Roberto ; Reis, Guilherme H. ^[1] ; Stolerman, Lucas M. ^[2]

Afiliação do(s) autor(es)

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

^[2] Univ Calif San Diego, Dept Mech & Aerosp Engn, San Diego, CA 92093 - USA

• Tipo de documento: Artigo Científico
• Fonte: ELECTRONIC JOURNAL OF PROBABILITY; v. 25, 2020.
• Citações Web of Science: 0

Resumo

We prove limit theorems for systems of interacting diffusions on sparse graphs. For example, we deduce a hydrodynamic limit and the propagation of chaos property for the stochastic Kuramoto model with interactions determined by Erdos-Renyi graphs with constant mean degree. The limiting object is related to a potentially infinite system of SDEs defined over a Galton-Watson tree. Our theorems apply more generally, when the sequence of graphs ({''}decorated{''} with edge and vertex parameters) converges in the local weak sense. Our main technical result is a locality estimate bounding the influence of far-away diffusions on one another. We also numerically explore the emergence of synchronization phenomena on Galton-Watson random trees, observing rich phase transitions from synchronized to desynchronized activity among nodes at different distances from the root. (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