5 papers · 1 filter
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…
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 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…