Estimation of the randomness of figure overlap
type: Item
instance of: scholarly article
title: Estimation of the randomness of figure overlap
zbMATH Open document ID: 0916.93072
author: N. B. Vasil'ev
author: A. M. Leontovich
published in: Problems of Information Transmission
publication date: 1999-07-12T00:00:00Z
review text: The problems considered in the paper arose from methods aimed at answering the question of to what extent a configuration of biological objects (cells) observed in a field of vision is random. Estimates for the variance of the intersection area for cells of a given shape randomly placed in a field of vision are presented. For this, several geometric theorems of isoperimetric type are proved. Estimates for arbitrary moments of figure-intersection areas are also obtained. Based on them, the central limit theorem is proved under some additional assumptions (figures are assumed to be small and round enough).
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 68T10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 92B99
zbMATH DE Number: 1253955
zbMATH Keywords: central limit theorem
zbMATH Keywords: torus
zbMATH Keywords: hypergraph
zbMATH Keywords: biological objects
zbMATH Keywords: random configuration
zbMATH Keywords: figure overlap
zbMATH Keywords: vision
reviewed by: Vyacheslav A. Vasiliev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1253955