Dynamics of a Fleming-Viot type particle system on the cycle graph - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Dynamics of a Fleming-Viot type particle system on the cycle graph

Résumé

This work is devoted to the study of interacting asymmetric continuous time random walks on the cycle graph, with uniform killing. The process is of Fleming-Viot or Moran type and allows to approximate the quasi-stationary distribution of a related process. We show that this model has a remarkable exact solvability, despite the fact that it is non-reversible with non-explicit invariant distribution. Our main results include quantitative propagation of chaos and exponential ergodicity with explicit constants, as well as formulas for covariances at equilibrium in terms of the Chebyshev polynomials. In particular we obtain a uniform bound in time for the convergence of the proportion of particles in each state when the number of particles goes to infinity. This work extends previous works by Cloez and Thai around the complete graph. It can be seen as a further step towards the study of such processes on graphs with general geometry.
Fichier principal
Vignette du fichier
2019-12-20-The cycle graph.pdf (371.9 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02447747 , version 1 (21-01-2020)
hal-02447747 , version 2 (26-01-2021)
hal-02447747 , version 3 (09-04-2021)

Identifiants

Citer

Josué M. Corujo. Dynamics of a Fleming-Viot type particle system on the cycle graph. 2020. ⟨hal-02447747v1⟩
158 Consultations
89 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More