Moments of sums of exponentials, beyond CHS
Abstract
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 theorem (1976) for completely homogeneous polynomials. We determine the exact regime of $p$ where such sums enjoy Schur-monotonicity.
Fields of Study & Subjects
Mathematical Inequalities and Applications
Probability and Statistical Research
Point processes and geometric inequalities
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 3 February 2026
- Document type
- Preprint