24 citations · 36 across the 11 of their papers we have counts for
4 papers · 1 filter
Dichotomies, structure, and concentration in normed spaces
Grigoris Paouris, Petros Valettas
We use probabilistic, topological and combinatorial methods to establish the following deviation inequality: For any normed space there exists an inve…
On the tightness of Gaussian concentration for convex functions
Petros Valettas
The concentration of measure phenomenon in Gauss' space states that every -Lipschitz map on satisfies \[ γ_{n} \left(\{ x : | f(x) - M_{f} | \geqslant t \} \ri…
Variance estimates and almost Euclidean structure
Grigoris Paouris, Petros Valettas
We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on , which provide sharp distributional inequalities. In the…
On a quantitative reversal of Alexandrov's inequality
Grigoris Paouris, Peter Pivovarov, Petros Valettas
Alexandrov's inequalities imply that for any convex body , the sequence of intrinsic volumes is non-increasing (when suitably normalized). Milman's random…