Limit theory for planar Gilbert tessellations

• Autorzy: Schreiber T. , Soja N.
• Języki publikacji: EN

Abstrakty

EN

A Gilbert tessellation arises by letting linear segments (cracks) in R² 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 a 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.

Słowa kluczowe

EN

Gilbert crack tessellation; stabilizing geometric functionals; central limit theorem; law of large numbers

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2011
• Tom: Vol. 31, Fasc. 1
• Strony: 149--160
• Opis fizyczny: Bibliogr. 21 poz., wykr.

Twórcy

autor

Schreiber T.

• Faculty of Mathematics & Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

autor

Soja N.

• Faculty of Mathematics & Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

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