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Central limit theorem for Gibbsian \(U\)-statistics of facet processes. (English) Zbl 1413.60014

Summary: A special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic joint moments for interaction \(U\)-statistics are calculated and the central limit theorem is derived using the method of moments.

MSC:

60F05 Central limit and other weak theorems
60D05 Geometric probability and stochastic geometry
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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