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Majorization, Entropy and Concentration Inequalities for Discrete α-Concave Random Variables

  • Abdulmajeed Alqasem
  • Heshan Aravinda
  • Arnaud Marsiglietti
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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.

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Cite

BibTeXRIS
BibTeX
@misc{alqasem2026majorization,
  title = {{Majorization, Entropy and Concentration Inequalities for Discrete $α$-Concave Random Variables}},
  author = {Abdulmajeed Alqasem and Heshan Aravinda and Arnaud Marsiglietti},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05439},
  eprint = {2610.05439},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05439},
}
RIS
TY  - UNPB
TI  - Majorization, Entropy and Concentration Inequalities for Discrete α-Concave Random Variables
AU  - Abdulmajeed Alqasem
AU  - Heshan Aravinda
AU  - Arnaud Marsiglietti
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05439
UR  - https://arxiv.org/abs/2610.05439
AB  - 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.
ER  -