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H 1 Hyperplane tessellations in Euclidean and spherical spaces

Auteurs : Schneider, Rolf (Auteur de la Conférence)
CIRM (Editeur )

Résumé : Random mosaics generated by stationary Poisson hyperplane processes in Euclidean space are a much studied object of Stochastic Geometry, and their typical cells or zero cells belong to the most prominent models of random polytopes. After a brief review, we turn to analogues in spherical space or, roughly equivalently, in a conic setting. A given number of i.i.d. random hyperplanes through the origin in $\mathbb{R}^d$ generate a tessellation of $\mathbb{R}^d$ into polyhedral cones. The typical cone of this tessellation, called a 'random Schläfli cone', is the object of our study. We provide first moments and mixed second moments of some geometric functionals, and compute probabilities of non-trivial intersection of a random Schläfli cone with a fixed polyhedral cone, or of two independent random Schläfli cones.

Parts are joint work with Matthias Reitzner, others with Daniel Hug.

Codes MSC :
51M20 - Polyhedra and polytopes; regular figures, division of spaces
52A22 - Random convex sets and integral geometry
52A55 - Spherical and hyperbolic convexity
52B05 - Combinatorial properties of convex sets
60D05 - Geometric probability and stochastic geometry
52C35 - Arrangements of points, flats, hyperplanes

 Informations sur la Vidéo Langue : Anglais Date de publication : 25/05/17 Date de captation : 16/05/17 Collection : Research talks ; Geometry ; Probability and Statistics Format : MP4 Domaine : Probability & Statistics ; Geometry Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2017-05-16_Schneider.mp4 Informations sur la rencontre Nom de la rencontre : 19th workshop on stochastic geometry, stereology and image analysis / 19ème conférence en géométrie stochastique, stéréologie et analyse d'imagesOrganisateurs de la rencontre : Calka, Pierre ; Coeurjolly, Jean-François ; Coupier, David ; Estrade, Anne ; Molchanov, IlyaDates : 15/05/17 - 19/05/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1513.htmlCitation Data DOI : 10.24350/CIRM.V.19167803 Cite this video as: Schneider, Rolf (2017). Hyperplane tessellations in Euclidean and spherical spaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19167803 URI : http://dx.doi.org/10.24350/CIRM.V.19167803

### Voir aussi

Bibliographie

1. Hug, D., & Schneider, R. (2016). Random conical tessellations. Discrete & Computational Geometry, 56(2), 395-426 - http://dx.doi.org/10.1007/s00454-016-9788-0

2. Reitzner, M., & Schneider, R. (2016). On the cells in a stationary Poisson hyperplane mosaic. - https://arxiv.org/abs/1609.04230

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