Journal of Applied Mathematics and Stochastic Analysis 
Volume 11 (1998), Issue 3, Pages 369-376
doi:10.1155/S1048953398000306

On certain random polygons of large areas

Igor N. Kovalenko1,2

 1STORM UNL, 166-220 Holloway Road, London N7 8DB, United Kingdom
2V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of the Ukraïna, Ukraine
Received 1 April 1997; Revised 1 January 1998

Abstract

Consider the tesselation of a plane into convex random polygons determined by a unit intensity Poissonian line process. Let M(A) be the ergodic intensity of random polygons with areas exceeding a value A. A two-sided asymptotic bound exp{−2A/π+c0A16}<M(A)<exp{−2A/π+c1A16} is established for large A, where c0>2.096, c1>6.36.