Mean-field limit for particle systems with topological interactions
Dario Benedetto, Emanuele Caglioti, Stefano Rossi
TL;DR
This paper develops a new approach to derive the mean-field limit for particle systems with topological interactions, overcoming limitations of traditional methods, by adapting techniques from Trocheris's 1986 work on the Vlasov-Poisson equation.
Contribution
It introduces a novel method for establishing the mean-field limit in systems with topological interactions, extending Trocheris's techniques to multidimensional cases.
Findings
Successfully derived the mean-field limit for topologically interacting particles
Extended Trocheris's 1986 techniques to multidimensional systems
Provided a new analytical framework for complex particle interactions
Abstract
The mean-field limit for systems of self-propelled agents with topological interaction cannot be obtained by means of the usual Dobrushin approach. We get a result on this direction by adapting to the multidimensional case the techniques developed by Trocheris in 1986 to treat the Vlasov-Poisson equation in one dimension.
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Taxonomy
TopicsMicro and Nano Robotics · Advanced Thermodynamics and Statistical Mechanics · Gas Dynamics and Kinetic Theory