An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results exists on this problem and in particular the explicit form of the nonlinearity is not known. This paper reviews this subject, some of the main ideas to get the limit nonlinear PDE and provides both heuristic and numerical informations on the precise form of the nonlinearity which are new with respect to the literature and coherent with the few known informations.
On the Macroscopic limit of Brownian Particles with local interaction / Flandoli, F; Leocata, Marta; Ricci, C. - In: STOCHASTICS AND DYNAMICS. - ISSN 0219-4937. - 20:6(2020), pp. 1-24. [10.1142/S0219493720400079]
On the Macroscopic limit of Brownian Particles with local interaction
LEOCATA M
;
2020
Abstract
An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results exists on this problem and in particular the explicit form of the nonlinearity is not known. This paper reviews this subject, some of the main ideas to get the limit nonlinear PDE and provides both heuristic and numerical informations on the precise form of the nonlinearity which are new with respect to the literature and coherent with the few known informations.
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