Extremal Properties of Some Geometric Processes

J. Mecke
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J. Mecke: Friedrich-Schiller-Universität, Sektion Mathematik

A chapter in Stochastic and Integral Geometry, 1987, pp 61-69 from Springer

Abstract: Abstract In this paper some isoperimetric inequalities for stationary random tessellations are discussed. At first, classical results on deterministic tessellations in the Euclidean plane are extended to the case of random tessellations. An isoperimetric inequality for the random Poisson polygon is derived as a consequence of a theorem of Davidson concerning an extremal property of tessellations generated by random lines in R 2. We mention extremal properties of stationary hyperplane tessellations in R d related to Davidson’s result in case d = 2. Finally, similar problems for random arrangements of r-flats in R d are considered (r>d-1).

Keywords: 60D05; 60G55; Random tessellations; line processes; flat processes; Poisson polygon; isoperimetric; inequalities (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3921-9_4

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DOI: 10.1007/978-94-009-3921-9_4

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