Journal of Applied Probability
- J. Appl. Probab.
- Volume 51A (2014), 311-332.
Percolation on stationary tessellations: models, mean values, and second-order structure
We consider a stationary face-to-face tessellation X of Rd and introduce several percolation models by colouring some of the faces black in a consistent way. Our main model is cell percolation, where cells are declared black with probability p and white otherwise. We are interested in geometric properties of the union Z of black faces. Under natural integrability assumptions, we first express asymptotic mean values of intrinsic volumes in terms of Palm expectations associated with the faces. In the second part of the paper we focus on cell percolation on normal tessellations and study asymptotic covariances of intrinsic volumes of Z ∩ W, where the observation window W is assumed to be a convex body. Special emphasis is given to the planar case where the formulae become more explicit, though we need to assume the existence of suitable asymptotic covariances of the face processes of X. We check these assumptions in the important special case of a Poisson-Voronoi tessellation.
J. Appl. Probab., Volume 51A (2014), 311-332.
First available in Project Euclid: 2 December 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60G55: Point processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Last, Günter; Ochsenreither, Eva. Percolation on stationary tessellations: models, mean values, and second-order structure. J. Appl. Probab. 51A (2014), 311--332. doi:10.1239/jap/1417528483. https://projecteuclid.org/euclid.jap/1417528483