Limit theory for planar Gilbert tessellations

Details Limit theory for planar Gilbert tessellations Limit theory for planar Gilbert tessellations

2010-04-30

arxiv.org/abs/1005.0023v1

Mathematics

Probability

12 pages

Scientific paper

A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an already existing one, it stops growing in this direction. The resulting process tessellates the plane. The purpose of the present paper is to establish law of large numbers, variance asymptotics and a central limit theorem for geometric functionals of such tessellations. The main tool applied is the stabilization theory for geometric functionals.

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