A note on subgaussian estimates for linear functionals on convex bodies

@inproceedings{Giannopoulos2006ANO,
  title={A note on subgaussian estimates for linear functionals on convex bodies},
  author={A. Giannopoulos and A. Pajor and G. Paouris},
  year={2006}
}
  • A. Giannopoulos, A. Pajor, G. Paouris
  • Published 2006
  • Mathematics
  • 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 R n with volume one and center of mass at the origin, there exists x 6 0 such that |{y ∈ K : |h y,xi| > tkh� ,xik 1}| 6 exp(−ct 2 /log 2 (t + 1)) for all t > 1, where c > 0 is an absolute constant. The proof is based on the study of the Lq–centroid bodies of K. Analogous results hold true for general log-concave measures. 
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