S. Brazitikos

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math.PR2026

Moments of sums of exponentials, beyond CHS

Silouanos Brazitikos, Colin Tang, Tomasz Tkocz

We establish a sharp lower bound on the $L_{p}$ -norm of sums of independent exponential random variables with fixed variance, for $p \geq 2$ , thus extending Hunter's positivity theor…

math.PR2026

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 $I^¼$ . We identify and provide a missing justifi…

math.PR2025

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 $n$ and every integer $k \geq 1$ , we show that under the constraint $\sum_{i = 1}^{n} a_{i}^{2} = 1$ the g…

math.PR2025

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…

Moments of sums of exponentials, beyond CHS

Discrete log-concavity and threshold phenomena for atomic measures

Sharp inequalities for symmetric polynomials, Hunter's conjecture, and moments of exponential random variables

Sharp estimates for the CramÃ©r transform of log-concave measures and geometric applications