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math.PR2026
Quantitative CLTs for Geometric Statistics of Dependent Marked Point Processes
Tianshu Cong, Aihua Xia, J. E. Yukich
Given a geometric statistic expressible as a sum of scores which depend on local data, \citet{BYY19} established central limit theorems for centered and normalized versions of thes…
math.PR2026
Limit theory for Lipschitz-localized statistics in random geometric models
B. Błaszczyszyn, D. Yogeshwaran, J. E. Yukich
We study sums of locally dependent scores associated with general marked (i.e., labeled) Euclidean point processes. We introduce geometric mixing conditions on the underlying point…
math.PR2026
Second-order Poincaré inequalities and localization on the Poisson space
Tara Trauthwein, J. E. Yukich
Given a mean zero functional of a Poisson measure on a metric space, we apply the Malliavin-Stein method to establish sharpened second-order Poincaré inequalities for $F/\sqrt{…