Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 369-376

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

Copyright © 1998 Igor N. Kovalenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.