Random approximation of convex bodies.

Fernando Affentranger

Publicacions Matemàtiques (1992)

  • Volume: 36, Issue: 1, page 85-109
  • ISSN: 0214-1493

Abstract

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Problems related to the random approximation of convex bodies fall into the field of integral geometry and geometric probabilities. The aim of this paper is to give a survey of known results about the stochastic model that has received special attention in the literature and that can be described as follows:Let K be a d-dimensional convex body in Eucliden space Rd, d ≥ 2. Denote by Hn the convex hull of n independent random points X1, ..., Xn distributed identically and uniformly in the interior of K. If φ is a random variable on d-dimensional polytopes on Rd, we define the random variable φn by:φn = φ (conv {X1, ..., Xn}),where conv denotes the convex hull. Typical random variables studied in the literature are numbers of vertices and facets, volume, surface area and mean width. Our main interest concerns the study of the mathematical expectation E(φn) of φn.Some further stochastic models and other problems related to random points studied in the literature will be presented.

How to cite

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Affentranger, Fernando. "Aproximación aleatoria de cuerpos convexos.." Publicacions Matemàtiques 36.1 (1992): 85-109. <http://eudml.org/doc/41165>.

@article{Affentranger1992,
author = {Affentranger, Fernando},
journal = {Publicacions Matemàtiques},
keywords = {Probabilidades; Geometría estocástica; Juegos geométricos; Conjuntos convexos; random approximation of convex bodies; integral geometry},
language = {spa},
number = {1},
pages = {85-109},
title = {Aproximación aleatoria de cuerpos convexos.},
url = {http://eudml.org/doc/41165},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Affentranger, Fernando
TI - Aproximación aleatoria de cuerpos convexos.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 1
SP - 85
EP - 109
LA - spa
KW - Probabilidades; Geometría estocástica; Juegos geométricos; Conjuntos convexos; random approximation of convex bodies; integral geometry
UR - http://eudml.org/doc/41165
ER -

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