Majorization, Entropy and Concentration Inequalities for Discrete $α$-Concave Random Variables
Year: 2026
Type: preprint
Abstract: We establish a maximum-variance inequality for discrete $α$-concave random variables in the regime $-1/3<α<0$, extending corresponding results beyond the discrete log-concave setting. As applications, we obtain a reverse entropy power inequality and bounds for the Lévy concentration function. We further establish polynomial-type concentration inequalities, reflecting the heavy-tailed nature of the class. A main tool in our approach is a convex majorization principle that reduces the relevant extremal problems to suitable $α$-affine distributions.
Source: arXiv (Cornell University)
Institutions: King Saud University, University of Wyoming, University of Florida
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: King Saud University
OpenAlex ID: W7220681719