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**Superprocesses with coalescing Brownian spatial motion as large-scale limits.**
*(English)*
Zbl 1067.60085

Superprocesses of several types have been shown to arise as limits of various kinds of branching and interacting particle systems. A class of superprocesses with dependent spatial motion (SDSM) has been studied by several authors. In particular, D. A. Dawson, Z. Li and H. Wang [Electron. J. Probab. 6, Paper No. 25 (2001; Zbl 1008.60093)] stated that in the case of the purely atomic SDSM studied therein, a suitably rescaled limit would lead to a superprocess with coalescing spatial motion (SCSM), which seems to be a new phenomenon in this area, but this was not proved because some questions regarding the SCSM remained open. In this paper the above-mentioned statement is proved. The proof is based on one-dimensional excursions.

Reviewer: Louis G. Gorostiza (Mexico City)

### MSC:

60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |

60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |

60G57 | Random measures |

60K35 | Interacting random processes; statistical mechanics type models; percolation theory |