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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2018: 0.53

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Volume 19, Issue 2


On the cells in a stationary Poisson hyperplane mosaic

Matthias Reitzner / Rolf Schneider
Published Online: 2018-07-20 | DOI: https://doi.org/10.1515/advgeom-2018-0013


Let X be the mosaic generated by a stationary Poisson hyperplane process in ℝd. Under some mild conditions on the spherical directional distribution of (which are satisfied if the process is isotropic), we show that with probability one the set of cells (d-polytopes) of X has the following properties. The translates of the cells are dense in the space of convex bodies. Every combinatorial type of simple d-polytopes is realized infinitely often by the cells of X. A further result concerns the distribution of the typical cell.

Keywords: Poisson process; hyperplane; polyhedra; tiling

MSC 2010: Primary 60D05; Secondary 51M20; 52C22


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About the article

Received: 2016-09-14

Revised: 2017-02-27

Published Online: 2018-07-20

Published in Print: 2019-04-24

Communicated by: M. Henk

Citation Information: Advances in Geometry, Volume 19, Issue 2, Pages 145–150, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0013.

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