Electronic Journal of Probability

Recursive tree processes and the mean-field limit of stochastic flows

Tibor Mach, Anja Sturm, and Jan M. Swart

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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 Aldous and Bandyopadyay 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.

Article information

Electron. J. Probab., Volume 25 (2020), paper no. 61, 63 pp.

Received: 30 December 2018
Accepted: 20 April 2020
First available in Project Euclid: 13 May 2020

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Digital Object Identifier

Primary: 82C22: Interacting particle systems [See also 60K35]
Secondary: 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 [See also 82B43, 82C43]

mean-field limit recursive tree process recursive distributional equation endogeny interacting particle systems cooperative branching

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Mach, Tibor; Sturm, Anja; Swart, Jan M. Recursive tree processes and the mean-field limit of stochastic flows. Electron. J. Probab. 25 (2020), paper no. 61, 63 pp. doi:10.1214/20-EJP460. https://projecteuclid.org/euclid.ejp/1589335470

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