Large-population limits of non-exchangeable particle systems - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2024

Large-population limits of non-exchangeable particle systems

Abstract

A particle system is said to be non-exchangeable if two particles cannot be exchanged without modifying the overall dynamics. Because of this property, the classical mean-field approach fails to provide a limit equation when the number of particles tends to infinity. In this review, we present novel approaches for the large-population limit of non-exchangeable particle systems, based on the idea of keeping track of the identities of the particles. These can be classified in two categories. The non-exchangeable mean-field limit describes the evolution of the particle density on the product space of particle positions and labels. Instead, the continuum limit allows to obtain an equation for the evolution of each particle's position as a function of its (continuous) label. We expose each of these approaches in the frameworks of static and adaptive networks.
Fichier principal
Vignette du fichier
Review_NonExchangeableParticleSystems.pdf (889.47 Ko) Télécharger le fichier
main.pdf (936.85 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04394768 , version 1 (15-01-2024)

Identifiers

Cite

Nathalie Ayi, Nastassia Pouradier Duteil. Large-population limits of non-exchangeable particle systems. 2024. ⟨hal-04394768⟩
40 View
16 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More