5 papers · 1 filter
Regular functional covering numbers
Apostolos Giannopoulos, Natalia Tziotziou
We establish the existence of a regular functional -position, in the sense of Pisier, for geometric log-concave functions. This provides a functional analogue of Pisier's regula…
Sections and projections of the outer and inner regularizations of a convex body
Natalia Tziotziou
We establish new geometric inequalities comparing the volumes of sections and projections of a convex body, whose barycenter or Santaló point is at the origin, with those of its in…
On the deterministic interior body of random polytopes
Minas Pafis, Natalia Tziotziou
Let be a sequence of independent copies of a random vector in . We revisit the question to determine the asymptotic shape of the random p…
Inequalities for sections and projections of log-concave functions
Natalia Tziotziou
We provide extensions of geometric inequalities about sections and projections of convex bodies to the setting of integrable log-concave functions. Namely, we consider suitable gen…
Moments of the Cramér transform of log-concave probability measures
Apostolos Giannopoulos, Natalia Tziotziou
Let be a centered log-concave probability measure on and let denote the Cramér transform of , i.e. $Λ_μ^{\ast}(x)=\sup\{\langle x,ξ\rangle-Λ_μ(ξ…