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

Preprint
Publisher Website
Google Scholar
  • 15 July 2006
Abstract
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.

This publication has 0 references indexed in Scilit: