This is an announcement for the paper "On the complexity of the set of unconditional convex bodies" by Mark Rudelson.

Abstract: We show that for any t>1, the set of unconditional convex bodies in R^n contains a t-separated subset of cardinality at least 0.1 exp exp (C(t) n). This implies that there exists an unconditional convex body in R^n which cannot be approximated within the distance d by a projection of a polytope with N faces unless N > exp(c(d)n). We also show that for t>2, the cardinality of a t-separated set of completely symmetric bodies in R^n does not exceed exp exp (c(t)(log n)^2).

Archive classification: math.MG math.FA

Remarks: 17 pages

Submitted from: rudelson@umich.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1410.0092

or

http://arXiv.org/abs/1410.0092