On particlesize distribution of convex similar bodies in $\mathbb{R}^3$
Abstract
We give an explicit form of particlesize distributions of convex similar bodies for random plane and random line, which naturally generalize famous Wicksell's corpuscle problem. The results are achieved by applying the Method of Model Solutions for solving wellknown Santaló's integral equations. We also give a partial result related to the question of existence and uniqueness of these solutions. We finally illustrate our approach on several examples.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.01663
 Bibcode:
 2019arXiv191201663K
 Keywords:

 Mathematics  Probability;
 45E99;
 45D05;
 60D05