2019/09/29 by Marcel Fenzl, Fenzl, Marcel
Mathematics · #05C80 #52A22 (Secondary) #60D05 (Primary) 60G55 #60F10 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1909.13274
openalex publication_date 2019/09/29 · openalex created_date 2019/10/03 · openalex updated_date 2026/07/28
We establish precise bounds on cumulants for a rather general class of non-linear geometric functionals satisfying the stabilization property under a simple, stationary (marked) point process admitting fast decay of its correlation functions and thereby conclude a Berry-Esseen bound, a concentration inequality, a moderate deviation principle and a Marcinkiewicz-Zygmund-type strong law of large numbers. The result is applied to the germ-grain model as well as to random sequential absorption for α-determinantal point processes having fast decaying kernels and certain Gibbsian point processes. The proof relies on cumulant expansions using a clustering result as well as factorial moment expansions for point processes.