Point process convergence for symmetric functions of high-dimensional random vectors

2023/03/28 by Johannes Heiny, Heiny, Johannes, Carolin Kleemann +1
Mathematics · #Point processes and geometric inequalities #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.2303.15804

Abstract

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint distribution of a fixed number of upper order statistics. As applications of the result a generalization of maximum convergence to point process convergence is given for simple linear rank statistics, rank-type U-statistics and the entries of sample covariance matrices.

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