Higher-dimensional light-tailed unbounded marks

Determine the asymptotic behavior of large inradii, nuclei, and marks in Poisson–Laguerre tessellations generated by light-tailed but possibly unbounded marks in dimensions d≥3.

Background

The paper establishes point-process convergence and maximal-inradius asymptotics for bounded marks in all dimensions d≥2, for sufficiently light-tailed marks in the planar case d=2, and for power-law marks in dimensions d≥2. The authors emphasize that bounded marks exhibit different behavior in the planar and higher-dimensional settings, and explicitly identify the extension to light-tailed yet unbounded marks in higher dimensions as unresolved.

References

The behavior for bounded marks is still very similar to that for constant marks, i.e., for Poisson--Voronoi tessellations, but we already observe a different behavior for the planar case and higher dimensional cases, triggering the question what happens to light-tailed but possibly unbounded marks in higher dimensions.

— Point process convergence of large inradii of Poisson-Laguerre tessellations  (2609.20750 - Schulte et al., 17 Sep 2026) in Section 1, Introduction and main results