Abstract

Let denote the divided difference of the exponential function. (i) We prove that exponential divided differences are log-submodular. (ii) We establish the four-point inequality $ \exp[a,a,b,c]\,\exp[d,d,b,c]+\exp[b,b,a,d]\,\exp[c,c,a,d]-\exp[a,b,c,d]^2 \ge 0 $ for all . (iii) We obtain sharp two-sided bounds for at fixed mean and variance; as a consequence, we derive their large-input asymptotics. (iv) We present closed-form identities for divided differences of the exponential function, including a convolution identity and summation formulas for repeated arguments.

Date

October 12, 2025

Authors

Qiulin Zeng, Nicholas Ezzell, Arman Babakhani, Itay Hen, Lev Barash

Journal

arXiv preprint arXiv:2510.10724