Concentration of mass and central limit properties of isotropic convex bodies Conference Paper uri icon

abstract

  • We discuss the following question: Do there exist an absolute constant c > 0 c>0 and a sequence ( n ) phi (n) tending to infinity with n n , such that for every isotropic convex body K K in R n {mathbb R}^n and every t 1 tgeq 1 the inequality Prob ( { x K : x 2 c n L K t } ) exp ( ( n ) t ) extrm {Prob}left (\big { xin K:| x|_2geq csqrt {n}L_Kt\big }
    ight ) leq exp \big (-phi (n)t\big )
    holds true? Under the additional assumption that K K is 1-unconditional, Bobkov and Nazarov have proved that this is true with ( n ) n phi (n)simeq sqrt

published proceedings

  • PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

author list (cited authors)

  • Paouris, G.

citation count

  • 10

complete list of authors

  • Paouris, G

publication date

  • February 2005