0-Pierced Triangles within a Poisson Overlay
History and Overview
2019-04-26 v2
Abstract
Let the Euclidean plane be simultaneously and independently endowed with a Poisson point process and a Poisson line process, each of unit intensity. Consider a triangle T whose vertices all belong to the point process. The triangle is 0-pierced if no member of the line process intersects any side of T. Our starting point is Ambartzumian's 1982 joint density for angles of T; our exposition is elementary and raises several unanswered questions.
Cite
@article{arxiv.1804.01353,
title = {0-Pierced Triangles within a Poisson Overlay},
author = {Steven R. Finch},
journal= {arXiv preprint arXiv:1804.01353},
year = {2019}
}
Comments
10 pages, 7 figures