Asymptotics for other mark-distribution classes

Determine the asymptotic behavior of large inradii, nuclei, and marks for classes of Poisson–Laguerre mark distributions other than the light-tailed and power-law classes studied in the paper.

Background

The paper treats light-tailed and power-law mark distributions as two extremal regimes, obtaining qualitatively different limiting behavior: Gumbel limits for the light-tailed settings considered and Fréchet limits for power-law marks. The authors explicitly leave unresolved what asymptotic behavior should arise for other classes of mark distributions.

References

Since one can think of the light-tailed and power-law mark distributions as two extremal cases, it also begs the question what one can expect for other classes of mark distributions.

— 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