Tagged particles and size-biased dynamics in mean-field interacting particle systems
arxiv(2024)
摘要
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.
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