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Segmentos al azar en Eⁿ

Let En be the Euclidean space of n dimensions. We consider sets of line segments given at random in En with the origin and direction uniformly distributed and with a given length distribution dF (l) (0 < l < [infinit]). We first consider the problem of finding the probability that a segment which intersects a given convex body Q have 0, 1 or 2 common points with the boundary of Q. Then we consider a Poisson process of segments of intensity [lamda] and solve some problems, in particular, that of finding the Distribution of the distance from a fixed point, chosen independently of the process, to the nearest end of the line segments. For n = 1, 2, 3 this last problem has been solved by R. Coleman. Finally, we add some comments on random trees in En

Facultad de Ciencias Exactas y Tecnología de la Universidad Nacional de Tucumán

Autor: Santaló, Lluís
Data: 1976
Resum: Let En be the Euclidean space of n dimensions. We consider sets of line segments given at random in En with the origin and direction uniformly distributed and with a given length distribution dF (l) (0 < l < [infinit]). We first consider the problem of finding the probability that a segment which intersects a given convex body Q have 0, 1 or 2 common points with the boundary of Q. Then we consider a Poisson process of segments of intensity [lamda] and solve some problems, in particular, that of finding the Distribution of the distance from a fixed point, chosen independently of the process, to the nearest end of the line segments. For n = 1, 2, 3 this last problem has been solved by R. Coleman. Finally, we add some comments on random trees in En
Format: application/pdf
ISSN: 0080-2360
Altres identificadors: Santaló, L. (1976). Segmentos al azar en Eⁿ. Revista de la Universidad Nacional de Tucumán: Serie A: Matemática y Física Teórica, 26 (1-2), 229-238
Accés al document: http://hdl.handle.net/10256.2/8283
Llenguatge: spa
Editor: Facultad de Ciencias Exactas y Tecnología de la Universidad Nacional de Tucumán
Drets: Tots els drets reservats
Títol: Segmentos al azar en Eⁿ
Tipus: article
Repositori: DUGiFonsEspecials

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