A note on subgaussian estimates for linear functionals on convex bodies Academic Article uri icon

abstract

  • We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If K is a convex body in ℝn with volume one and center of mass at the origin, there exists x ≠ 0 such that |{y ∈ K: |(y, x) | ≥ t||(̇, x)||1}≤ exp(-ct2/log2 (t + 1)) for all t ≥ 1, where c > 0 is an absolute constant. The proof is based on the study of the L q-centroid bodies of K. Analogous results hold true for general log-concave measures. © 2007 American Mathematical Society.

author list (cited authors)

  • Giannopoulos, A., Pajor, A., & Paouris, G.

citation count

  • 8

publication date

  • March 2007