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0-Pierced Triangles within a Poisson Overlay
Published 4 Apr 2018 in math.HO | (1804.01353v2)
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.
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