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arXiv · 2610.06372

Functional central limit theorems for Laguerre tessellations

Chinmoy Bhattacharjee·Anna Gusakova·Christian Hirsch
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Abstract

We study empirical processes of observable extreme generators in stationary Poisson-Laguerre tessellations, with each generator weighted either by one or by the volume of its cell. Under moment assumptions that allow heavy-tailed marks, we prove functional central limit theorems as the observation window grows, on compact intervals where the mark law has a bounded density. We also obtain covariance asymptotics with a surface-order error and quantitative univariate and multivariate Gaussian approximation.

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Chinmoy Bhattacharjee, Anna Gusakova, Christian Hirsch. 2026-10-05. Functional central limit theorems for Laguerre tessellations. https://arxiv.org/abs/2610.06372

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