This is an announcement for the paper "On approximations by projections of polytopes with few facets" by Alexander E. Litvak, Mark Rudelson, and Nicole Tomczak-Jaegermann.

Abstract: We provide an affirmative answer to a problem posed by Barvinok and Veomett, showing that in general an n-dimensional convex body cannot be approximated by a projection of a section of a simplex of a sub-exponential dimension. Moreover, we establish a lower bound of the Banach-Mazur distance between n-dimensional projections of sections of an N-dimensional simplex and a certain convex symmetric body, which is sharp up to a logarithmic factor for all N>n.

Archive classification: math.FA math.MG

Mathematics Subject Classification: Primary: 52A23, 52A27, Secondary: 52B55, 46B09

Remarks: 22 pages

Submitted from: rudelson@umich.edu

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

http://front.math.ucdavis.edu/1209.6281

or

http://arXiv.org/abs/1209.6281