Recursive tree processes and the mean-field limit of stochastic flows. (English) Zbl 1446.82054

Summary: Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We consider interacting particle systems on the complete graph in the mean-field limit, i.e., as the number of vertices tends to infinity. We are not only interested in the mean-field limit of a single process, but mainly in how several coupled processes behave in the limit. This turns out to be closely related to recursive tree processes as studied by D. J. Aldous and A. Bandyopadhyay [Ann. Appl. Probab. 15, No. 2, 1047–1110 (2005; Zbl 1105.60012)] in discrete time. We here develop an analogue theory for recursive tree processes in continuous time. We illustrate the abstract theory on an example of a particle system with cooperative branching. This yields an interesting new example of a recursive tree process that is not endogenous.


82C22 Interacting particle systems in time-dependent statistical mechanics
60J25 Continuous-time Markov processes on general state spaces
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60K35 Interacting random processes; statistical mechanics type models; percolation theory


Zbl 1105.60012
Full Text: DOI arXiv Euclid


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