Tagged particles and size-biased dynamics in mean-field interacting particle systems

2024/03/27 by Angeliki Koutsimpela, Stefan Großkinsky, Koutsimpela, Angeliki +1 · 2 citations
Materials Science · Physics and Astronomy · Mathematics · #Material Dynamics and Properties #Theoretical and Computational Physics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2403.18179

Abstract

We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the occupation number on the tagged particle site converges to a time-inhomogeneous Markov process with non-linear master equation given by the law of large numbers of size-biased empirical measures. The latter are important in recent efforts to understand the dynamics of condensation in interacting particle systems.

Cited by

• Mean-field limits in interacting particle systems with symmetric superlinear rates
• Modulated Poisson-Dirichlet diffusions arising from inclusion processes with a slow phase

Related

• Finite Size Fluctuations in Interacting Particle Systems
• Interacting particle systems with long range interactions: approximation by tagged particles in random fields
• On the mean field limit of the Random Batch Method for interacting particle systems
• Large-scale behavior of a particle system with mean-field interaction: Traveling wave solutions
• Mean-field limits in interacting particle systems with symmetric superlinear rates