Combinatorial Decompositions and Homogeneous Geometrical Processes

V. K. Oganian
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V. K. Oganian: Yerevan State University, Department of Mathematics

A chapter in Stochastic and Integral Geometry, 1987, pp 71-81 from Springer

Abstract: Abstract This paper considers line processes and random mosaics. The processes are assumed invariant with respect to the group of translations of R 2. An expression for the probabilities πk(t, α), k = 0,1,2,… to have k hits on an interval of length t taken on a ‘typical line of direction α’ (the hits are produced by other lines of the process) is obtained. Also, the distribution of a length of a ‘typical edge having direction α’ in terms of the process {P i, ψi} is found, here P i is the point process of intersections of edges of the mosaic with a fixed line of direction α and the mark ψi is the intersection angle at P i. The method is based on the results of combinatorial integral geometry.

Keywords: 60D05; 60G55.; Line processes; random mosaics; combinatorial decompositions; marked point processes (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_5

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DOI: 10.1007/978-94-009-3921-9_5

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