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Propagation of chaos for a system of annihilating Brownian spheres. (English) Zbl 0669.60094
N\(\gg 0\) Euclidean balls of some specified radius \(s_ N/2\) evolve according to independent Brownian motions in \({\mathbb{R}}^ d\), \(d\geq 2\), initially distributed with a bounded density function \(V\geq 0\). Colliding particles immediately disappear. Then this system of particles presents a propagation of chaos property with respect to the equation \[ \partial u/\partial t=2^{-1}\Delta u-c_ du^ 2,\quad u_{| t=0}=V \] (c\({}_ d>0\) is some constant). The used approach differs from that of R. Lang and Nguyen Xuan Xanh [Z. Wahrscheinlichkeitstheor. Verw. Geb. 54, 227-280 (1980; Zbl 0449.60074)]. We also refer to the meanwhile appeared related work of C. Boldrighini, A. De Masi, A. Pellegrinotti and E. Presutti [Stochastic Processes Appl. 25, 137-152 (1987; Zbl 0626.60103)]; P. Dittrich [Probab. Theory Relat. Fields 79, No.1, 115-128 (1988; Zbl 0631.60081)]; and G. Nappo, E. Orlandi and H. Rost [J. Stat. Phys. 55, No.3-4 (Spec. Issue), 579-600 (1989)].
Reviewer: K.Fleischmann

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J65 Brownian motion
35K55 Nonlinear parabolic equations
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