Balancing vectors and Gaussian measures of n-dimensional convex bodies

✍ Scribed by Wojciech Banaszczyk

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 169 KB
• Volume: 12
• Category: Article
• ISSN: 1042-9832
• DOI: 10.1002/(sici)1098-2418(199807)12:4<351::aid-rsa3>3.0.co;2-s

✦ Synopsis

Let и be the Euclidean norm on R and ␥ the standard Gaussian measure n n Ž . ynr2 y5x5 2 r2 on R with density 2 e . It is proved that there is a numerical constant c ) 0 n Ž . with the following property: if K is an arbitrary convex body in R with ␥ K G 1r2, then n n 5 5 5 5 to each sequence u , . . . , u gR with u , . . . , u Fc there correspond signs , . . . , 1 m 1 m 1 m

s"1 such that Ý m u g K. This improves the well-known result obtained by Spencer