منابع مشابه
Large Faces in Poisson Hyperplane Mosaics by Daniel Hug
A generalized version of a well-known problem of D. G. Kendall states that the zero cell of a stationary Poisson hyperplane tessellation in Rd , under the condition that it has large volume, approximates with high probability a certain definite shape, which is determined by the directional distribution of the underlying hyperplane process. This result is extended here to typical kfaces of the t...
متن کاملVertex Numbers of Weighted Faces in Poisson Hyperplane Mosaics
In the random mosaic generated by a stationary Poisson hyperplane process in R, we consider the typical k-face weighted by the j-dimensional volume of the j-skeleton (0 ≤ j ≤ k ≤ d). We prove sharp lower and upper bounds for its expected number of vertices.
متن کاملWeighted Poisson–Delaunay Mosaics∗
Slicing a Voronoi tessellation in R with a k-plane gives a k-dimensional weighted Voronoi tessellation, also known as power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the k-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generate...
متن کاملTypical Cells in Poisson Hyperplane Tessellations
It is proved that the shape of the typical cell of a stationary and isotropic Poisson random hyperplane tessellation is, with high probability, close to the shape of a ball if the kth intrinsic volume (k ≥ 2) of the typical cell is large. The shape of typical cells of large diameter is close to the shape of a segment.
متن کاملSecond moments related to Poisson hyperplane tessellations
It is well known that the vertex number of the typical cell of a stationary hyperplane tessellation in R has, under some mild conditions, an expectation equal to 2, independent of the underlying distribution. The variance of this vertex number can vary widely. Under Poisson assumptions, we give sharp bounds for this variance, showing, in particular, that its maximum is attained if and only if t...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2010
ISSN: 0091-1798
DOI: 10.1214/09-aop510