11 papers
Thin-Shell implies small-ball deviation via Gaussian tilts
Silouanos Brazitikos, Emanuel Milman
We show that uniform thin-shell estimates for (even) isotropic log-concave measures on yield precise and explicit deviation estimates for the Euclidean norm $|X|…
Geometric Bounds for the Mean Gauge and the Mean Width in Isotropic Position
Silouanos Brazitikos, Christos Pandis
Let be an origin-symmetric convex body and assume that its uniform probability measure is isotropic in the probabilistic normalization, namely \[ \int_K x…
Sharp Estimates for Conjugate Functions with Applications to Trigonometric Polynomials
Silouanos Brazitikos
We prove a sharp estimate for conjugate functions using a harmonic majorant in a half-strip. As an application, we remove the logarithmic loss from a theorem of Papadopoulos on min…
On Sections of Convex Bodies in John's Position and of Generalised Balls
David Alonso-Gutiérrez, Silouanos Brazitikos, Giorgos Chasapis
We revisit an ingenious argument of K. Ball to provide sharp estimates for the volume of sections of a convex body in John's position. Our technique combines the geometric Brascamp…
On the maximal perimeter of isotropic log-concave probability measures
Silouanos Brazitikos, Apostolos Giannopoulos, Antonios Hmadi +1
We study the maximal perimeter constant of isotropic log-concave probability measures on . For a measure , this quantity, denoted by , is defined as the s…
Moments of sums of exponentials, beyond CHS
Silouanos Brazitikos, Colin Tang, Tomasz Tkocz
We establish a sharp lower bound on the -norm of sums of independent exponential random variables with fixed variance, for , thus extending Hunter's positivity theor…