[Visibility in the Boolean model]
The aim of this Note is to give an estimate on the tail probability of the visibility function in a Boolean model: this function is defined as the length of the longest ray starting at the origin that does not intersect an obstacle. Convergence results are added, when the size of obstacles goes to zero and when the distance between the origin and the closest obstacle goes to infinity.
Le but de cette Note est de fournir une estimation fine de la queue de la loi de probabilité de la visibilité dans un modèle Booléen : cette fonction est définie comme étant la longueur du plus grand rayon issu de l'origine n'intersectant pas d'obstacle. L'étude est complétée par des résultats de convergence lorsque la taille des obstacles tend vers 0 et lorsque la distance de l'origine au plus proche obstacle tend vers l'infini.
Accepted:
Published online:
@article{CRMATH_2009__347_11-12_659_0,
author = {Calka, Pierre and Michel, Julien and Porret-Blanc, Sylvain},
title = {Visibilit\'e dans le mod\`ele {Bool\'een}},
journal = {Comptes Rendus. Math\'ematique},
pages = {659--662},
publisher = {Elsevier},
volume = {347},
number = {11-12},
year = {2009},
doi = {10.1016/j.crma.2009.03.018},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.03.018/}
}
TY - JOUR AU - Calka, Pierre AU - Michel, Julien AU - Porret-Blanc, Sylvain TI - Visibilité dans le modèle Booléen JO - Comptes Rendus. Mathématique PY - 2009 SP - 659 EP - 662 VL - 347 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.03.018/ DO - 10.1016/j.crma.2009.03.018 LA - fr ID - CRMATH_2009__347_11-12_659_0 ER -
%0 Journal Article %A Calka, Pierre %A Michel, Julien %A Porret-Blanc, Sylvain %T Visibilité dans le modèle Booléen %J Comptes Rendus. Mathématique %D 2009 %P 659-662 %V 347 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.03.018/ %R 10.1016/j.crma.2009.03.018 %G fr %F CRMATH_2009__347_11-12_659_0
Calka, Pierre; Michel, Julien; Porret-Blanc, Sylvain. Visibilité dans le modèle Booléen. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 659-662. doi : 10.1016/j.crma.2009.03.018. http://www.numdam.org/articles/10.1016/j.crma.2009.03.018/
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