Weighted faces of Poisson hyperplane tessellations
نویسندگان
چکیده
منابع مشابه
Vertex 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.
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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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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.
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We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in R d. This result generalizes an earlier one proved by Paroux [Adv. for intersection points of motion-invariant Poisson line processes in R 2. Our proof is based on Hoeffd-ing's decomposition of U-statistics which seems to be more efficient and adequate to tackle...
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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...
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2009
ISSN: 0001-8678,1475-6064
DOI: 10.1017/s0001867800003529