One-sided concentration near the mean of log-concave distributions
Iosif Pinelis·2026-02-06·via math.PR updates on arXiv.org
A lower bound on the probability $P(0<X<δ)$ for all real $δ>0$ and all random variables $X$ with log-concave p.d.f.'s such that $EX=0$ and $EX^2=1$ is obtained.