Small ball probability estimates, 2-behavior and the hyperplane conjecture Academic Article uri icon

abstract

  • We introduce a method which leads to upper bounds for the isotropic constant. We prove that a positive answer to the hyperplane conjecture is equivalent to some very strong small probability estimates for the Euclidean norm on isotropic convex bodies. As a consequence of our method, we obtain an alternative proof of the result of J. Bourgain that every 2-body has bounded isotropic constant, with a slightly better estimate: If K is a symmetric convex body in Rn such that {norm of matrix} , {norm of matrix}q {norm of matrix} , {norm of matrix}2 for every Sn - 1 and every q 2, then LK C sqrt(log ), where C > 0 is an absolute constant. 2009.

published proceedings

  • Journal of Functional Analysis

author list (cited authors)

  • Dafnis, N., & Paouris, G.

citation count

  • 24

complete list of authors

  • Dafnis, Nikos||Paouris, Grigoris

publication date

  • March 2010