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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{bhattacharjee2026functional,
  title = {{Functional central limit theorems for Laguerre tessellations}},
  author = {Chinmoy Bhattacharjee and Anna Gusakova and Christian Hirsch},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06372},
  eprint = {2610.06372},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06372},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Functional central limit theorems for Laguerre tessellations
AU  - Chinmoy Bhattacharjee
AU  - Anna Gusakova
AU  - Christian Hirsch
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06372
UR  - https://arxiv.org/abs/2610.06372
AB  - 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.
ER  -