A note on the length,measured along fixed orientations,of a path connecting any two points relative to their straight line distance |
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| Authors: | Pieter H A J M van Gelder |
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| Institution: | Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628CN Delft, The Netherlands |
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| Abstract: | Let D be an invertible matrix and L1 (x) denote the well‐known 1‐norm of x∈Rn. In this note we analyse the kth moment of the ratio L1 (D?1z) and its asymptotics in special cases, where z is uniformly distributed over the unit hypersphere. Conceptually, L1 (D?1z) can be seen as the (weighted) length, measured along fixed orientations, of a path connecting any two points relative to their straight line distance. |
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| Keywords: | statistical geometry ratio of L1 to L2‐norm |
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