We investigate geometric and functional inequalities for the class of log-concave probability
sequences. We prove dilation inequalities for log-concave probability measures on the …

We explore probability distributions on the real line whose Laplace transform admits an
upper bound of subgaussian type known as strict subgaussianity. One class in this family …

We prove an extension of Szarek's optimal Khinchin inequality (1976) for distributions close
to the Rademacher one, when all the weights are uniformly bounded by a 1/2 fraction of their …

We develop the notion of discrete degrees of freedom of a log-concave sequence and use it
to prove that geometric distribution minimises Rényi entropy of order infinity under fixed …

For normalized sums $ Z_n $ of iid random variables, we explore necessary and sufficient
conditions which guarantee the normal approximation with respect to the R\'enyi divergence …

1 Introduction and results Page 1 SHARP BOUNDS ON P-NORMS FOR SUMS OF
INDEPENDENT UNIFORM RANDOM VARIABLES, 0 < P < 1 By GIORGOS CHASAPIS …

We establish a sharp comparison inequality between the negative moments and the second
moment of the magnitude of sums of independent random vectors uniform on three …