Combinatorial principles in stochastic geometry in the plane: A review
type: Item
instance of: scholarly article
title: Combinatorial principles in stochastic geometry in the plane: A review
zbMATH Open document ID: 1171.60004
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 2008-09-22T00:00:00Z
review text: The author gives a review on some combinatorial principles in Stochastic Geometry in the plane; he mainly underlines some results, obtained in Yerevan, concerning tomography of random processes of lines, random tessellations and Boolean models in the plane. The required invariance is either with respect to the group \(T\) of translations or to the group \(M\) of the motions of \(\mathbb{R}^2\). After recalling basic concepts on translation invariant line processes, the modified Palm formulas and the method of invariant embedding are described. The author also states the condition implying Poissonity on the point process of intersections induced on a test line. Moreover, the method of integration of a combinatorial decomposition is described and the method based on summation of Pleijel-type identities is applied to random Boolean models invariant with respect to the group \(M\) of the Euclidean motions in \(\mathbb{R}^2\). An example of application of the method of invariant embedding, consisting of integration a combinatorial decomposition and derivation of a differential identity for the probability distribution of the number of hits of a test segment by the random lines, is also given.
reviewed by: Loredana Sorrenti
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 52A22
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G07
zbMATH DE Number: 5345590
zbMATH Keywords: combinatorial decomposition
zbMATH Keywords: invariant imbedding
zbMATH Keywords: random geometrical processes
zbMATH Keywords: random tessellation
zbMATH Keywords: Palm probabilities
author: Viktor Ohanyan
MaRDI profile type: Publication
full work available at URL: s11957-008-1003-z
OpenAlex ID: W2014420837
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DOI: 10.3103/S11957-008-1003-Z
description: scientific article; zbMATH DE number 5345590