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

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