Anti-concentration inequalities for log-concave variables on the real line

Abstract

We prove sharp anti-concentration results for log-concave random variables on the real line in both the discrete and continuous setting. Our approach is elementary and uses majorization techniques to recover and extend some recent and not so recent results.

For the special volume of the XIV Symposium of Probability and Stochastic Processes CIMAT, Mexico, November 20-24, 2023