On the domain of attraction for the lower tail in Wicksell's corpuscle problem

TL;DR

This paper investigates the lower tail behavior of sphere radii distributions in Wicksell's problem, analyzing how their domains of attraction relate across different dimensions and sections.

Contribution

It characterizes the relationships between the domains of attraction for lower tails of sphere radii distributions in various dimensions within Wicksell's corpuscle problem.

Findings

Domains of attraction are interconnected across dimensions.

Lower tail behaviors depend on the geometric configuration.

Results clarify the tail behavior in spherical and sectional distributions.

Abstract

We consider the classical Wicksell corpuscle problem with spherical particles in R^n and investigate the shapes of lower tails of distributions of `sphere radii' in R^n and `sphere radii' in a k-dimensional section plane. We show in which way the domains of attraction are related to each other.