A **discrete** distribution $p$ over $\mathbb{N}$ is said to be *log-concave* if it satisfies the following conditions:

- The support of $p$ is a contiguous interval, i.e. $\exists a \leq b$ s.t. $p_i > 0$ iff $a\leq i \leq b$.
- for all $i\in\mathbb{N}$, $p_i^2 \geq p_{i-1}p_{i+1}$.

(in the literature, condition (1) is sometimes forgotten). This is the discrete analogue of continuous log-concave densities, and includes many families of usual discrete distributions.

What I am looking for is a set of lecture notes, papers or more generally references that provides an exhaustive (or as comprehensive as possible) list of theorems and properties of discrete log-concave distributions. As for now, I am aware of Devroye '87 and (part of) An '97, but not much more.

Thank you for your help!

J. Amer. Stat. Assoc., vol. 66, no. 334, 386-389. $\endgroup$ – cardinal Mar 15 '15 at 16:37