2012/09/27 by Alexander E. Litvak, Litvak, Alexander E., Mark Rudelson +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #46B09 #52A27 #Diffusion and Search Dynamics #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Metric Geometry (math.MG) #Point processes and geometric inequalities #Primary: 52A23 #Secondary: 52B55 #math.FA #math.MG #msc:46B09 #msc:52A23 #msc:52A27 #msc:52B55
paper · pdf · doi:10.48550/arxiv.1209.6281
22 pages
arxiv created 2012/09/27 · openalex publication_date 2012/09/27 · arxiv updated 2012/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.