Summary
Take the nth generation of a supercritical branching random walk (a spatially homogeneous branching process) as a process of cluster centres and take independent copies of some simple point process Y as the clusters. Let the resulting point process be Y n . For a given sequence of real numbers {x n } let Y n be centred on x n . Under certain conditions, when an appropriate scale change is made, the resulting point process converges in distribution to a non-trivial limit.
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Biggins, J.D. Limiting point processes in the branching random walk. Z. Wahrscheinlichkeitstheorie verw Gebiete 55, 297–303 (1981). https://doi.org/10.1007/BF00532121
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DOI: https://doi.org/10.1007/BF00532121