Author:
Jahnel Benedikt,Tóbiás András
Abstract
AbstractIn this paper we show existence of all exponential moments for the total edge length in a unit disk for a family of planar tessellations based on stationary point processes. Apart from classical tessellations such as the Poisson–Voronoi, Poisson–Delaunay and Poisson line tessellation, we also treat the Johnson–Mehl tessellation, Manhattan grids, nested versions and Palm versions. As part of our proofs, for some planar tessellations, we also derive existence of exponential moments for the number of cells and the number of edges intersecting the unit disk.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference20 articles.
1. Bollobás, B., Riordan, O.: Percolation on random Johnson-Mehl tessellations and related models. Probab. Theory Relat. Fields 140(3–4), 319–343 (2008)
2. Calka, P.: An explicit expression for the distribution of the number of sides of the typical Poisson-Voronoi cell. Adv. Appl. Probab. 35(4), 863–870 (2003)
3. Calka, P.: Tessellations. In: Kendall, W.S., Molchanov, I. (eds.) New Perspectives in Stochastic Geometry, pp. 145–169. Oxford University Press, Oxford (2010)
4. Chayes, J.T., Chayes, L., Kotecký, R.: The analysis of the Widom-Rowlinson model by stochastic geometric methods. Commun. Math. Phys. 172(3), 551–569 (1995)
5. Chiu, S., Stoyan, D., Kendall, W., Mecke, J.: Stochastic Geometry and Its Applications. Wiley, New York (2013)
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