Aproximación aleatoria de cuerpos convexos.

Título inglés Random approximation of convex bodies.
Título español Aproximación aleatoria de cuerpos convexos.
Autor/es Affentranger, Fernando
Organización Math. Inst. Albert-Ludwigs-Univ., Freiburg im Breisgau, Alemania
Revista 0214-1493
Publicación 1992, 36 (1): 85-109, 58 Ref.
Tipo de documento articulo
Idioma Español
Resumen inglés 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.
Clasificación UNESCO 120803
Palabras clave español Probabilidades ; Geometría estocástica ; Juegos geométricos ; Conjuntos convexos
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