Kinetic models for topological nearest-neighbor interactions

Blanchet, Adrien and Degond, Pierre (2017) Kinetic models for topological nearest-neighbor interactions. Journal of Statistical Physics, 169 (5). pp. 929-950.

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Official URL: http://tse-fr.eu/pub/32176

Abstract

We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal and human behavior. Precisely, the system consists of a finite number of particles characterized by their positions and velocities. At random times a randomly chosen particle, the follower adopts the velocity of its closest neighbor, the leader. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit kinetic equation is a non-standard spatial diffusion equation for the particle distribution function. We also study the case wherein the particles interact with their K closest neighbors and show that the corresponding kinetic equation is the same. Finally, we prove that these models can be seen as a singular limit of the smooth rank-based model previously studied in [10]. The proofs are based on a combinatorial interpretation of the rank as well as some concentration of measure arguments.

Item Type: Article
Language: English
Date: December 2017
Refereed: Yes
Uncontrolled Keywords: rank-based interaction, spatial diffusion equation, continuity equation, concentration of measure
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 13 Apr 2018 12:13
Last Modified: 13 Apr 2018 12:13
OAI ID: oai:tse-fr.eu:32176
URI: http://publications.ut-capitole.fr/id/eprint/25738

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