Counting faces of randomly-projected polytopes when the projection radically lowers dimension

Details Counting faces of randomly-projected polytopes when the projection radically lowers dimension Counting faces of randomly-projected polytopes when the projection radically lowers dimension

2006-07-15

arxiv.org/abs/math/0607364v2

Mathematics

Metric Geometry

56 pages

Scientific paper

This paper develops asymptotic methods to count faces of random high-dimensional polytopes. Beyond its intrinsic interest, our conclusions have surprising implications - in statistics, probability, information theory, and signal processing - with potential impacts in practical subjects like medical imaging and digital communications. Three such implications concern: convex hulls of Gaussian point clouds, signal recovery from random projections, and how many gross errors can be efficiently corrected from Gaussian error correcting codes.

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