COUNTING FACES OF RANDOMLY PROJECTED POLYTOPESWHEN THE PROJECTION RADICALLY LOWERS DIMENSION

摘要

This paper develops asymptoticmethods to count faces of random high-dimensional polytopes, a seemingly dryand unpromising pursuit. Yet our conclusions have surprising implications — instatistics, probability, information theory, and signal processing — with potentialimpacts in practical subjects like medical imaging and digital communications. Be-fore involving the reader in our lengthy analysis of high-dimensional face counting,we describe three implications of our results.