6 citations · 10 across the 20 of their papers we have counts for
27 papers
Hermite-Fisher bounds and stability for min-entropy power inequalities
Silouanos Brazitikos, Martin Rapaport, Tomasz Tkocz
We derive explicit lower bounds for relative Fisher information by combining a variational principle with suitably orthogonalized Hermite-polynomial test functions. The resulting c…
Thin-Shell implies small-ball deviation via Gaussian tilts
Silouanos Brazitikos, Emanuel Milman
We show that uniform thin-shell estimates for isotropic log-concave measures on yield precise and explicit deviation estimates for the Euclidean norm below…
Many Facets in Random Polytopes from Product and Log-Concave Measures
Silouanos Brazitikos, Minas Pafis
We prove bounds of order for the expected number of facets of high-dimensional random polytopes. First, let be a non-degenerate compactly supported even proba…
A Deterministic Proof of the Slicing Theorem
Silouanos Brazitikos
We give a deterministic proof of Bourgain's slicing theorem. The proof uses neither stochastic localization nor stochastic calculus, does not rely on Guan's covariance bound, and a…
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 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 supr…
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…
Discrete log-concavity and threshold phenomena for atomic measures
Silouanos Brazitikos, Minas Pafis
We investigate threshold phenomena for random polytopes $K_N=\conv\{X_1,\dots,X_N\}$ generated by i.i.d.\ samples from an atomic law . We identify and provide a missing justific…
Sharp inequalities for symmetric polynomials, Hunter's conjecture, and moments of exponential random variables
Silouanos Brazitikos, Christos Pandis
We prove Hunter's conjecture on complete homogeneous symmetric polynomials. For even and every integer , we show that under the constraint the g…
Sharp Estimates for some Integral-Geometric Quantities Related To Transversality, Curvature And Visibility
Silouanos Brazitikos, Dimitris-Marios Liakopoulos
We investigate integral-geometric quantities arising from harmonic analysis which measure visibility and transversality. Motivated by their applications in multilinear Kakeya probl…
List decoding of toric codes
Silouanos Brazitikos, Theodoulos Garefalakis, Eleni Tzanaki
Polynomial evaluation codes hold a prominent place in coding theory. In this work, we study the problem of list decoding for a general class of polynomial evaluation codes, also kn…
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…
Sharp estimates for the Cramér transform of log-concave measures and geometric applications
Silouanos Brazitikos, Giorgos Chasapis
We establish a new comparison between the Legendre transform of the cumulant generating function and the half-space depth of an arbitrary log-concave probability distribution on th…
On some integral-geometric quantities related to transversality, curvature and visibility
Silouanos Brazitikos, Anthony Carbery, Finlay McIntyre
We consider some integral-geometric quantities that have recently arisen in harmonic analysis and elsewhere, derive some sharp geometric inequalities relating them, and place them…
Threshold for the expected measure of random polytopes
Silouanos Brazitikos, Apostolos Giannopoulos, Minas Pafis
Let be a log-concave probability measure on and for any consider the random polytope , where are inde…
On a version of the slicing problem for the surface area of convex bodies
Silouanos Brazitikos, Dimitris-Marios Liakopoulos
We study the slicing inequality for the surface area instead of volume. This is the question whether there exists a constant depending (or not) on the dimension so that $…
Half-space depth of log-concave probability measures
Silouanos Brazitikos, Apostolos Giannopoulos, Minas Pafis
Given a probability measure on , Tukey's half-space depth is defined for any by , where ${\cal H}(x)…
Vector-Valued Maclaurin Inequalities
Silouanos Brazitikos, Finlay McIntyre
We investigate a Maclaurin inequality for vectors and its connection to an Aleksandrov-type inequality for parallelepipeds.
Sections of convex bodies in John's and minimal surface area position
David Alonso-Gutiérrez, Silouanos Brazitikos
We prove several estimates for the volume, mean width, and the value of the Wills functional of sections of convex bodies in John's position, as well as for their polar bodies. The…
On affine invariant and local Loomis-Whitney type inequalities
David Alonso-Gutiérrez, Julio Bernués, Silouanos Brazitikos +1
We prove various extensions of the Loomis-Whitney inequality and its dual, where the subspaces on which the projections (or sections) are considered are either spanned by vectors $…
Reverse Loomis-Whitney inequalities via isotropicity
David Alonso-Gutiérrez, Silouanos Brazitikos
Given a centered convex body , we study the optimal value of the constant such that there exists an orthonormal basis for whi…
On the average volume of sections of convex bodies
Silouanos Brazitikos, Susanna Dann, Apostolos Giannopoulos +1
The average section functional of a centered convex body in is the average volume of central hyperplane sections of : \begin{equation*}{\rm as}(K)=…
Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies
S. Brazitikos, A. Giannopoulos, D-M. Liakopoulos
The classical Loomis-Whitney inequality and the uniform cover inequality of Bollobás and Thomason provide lower bounds for the volume of a compact set in terms of its lower dimensi…