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Sharp estimates for the Cram\'{e}r transform of log-concave measures and geometric applications by Brazitikos, Silouanos; Chasapis, Giorgos is a scholarly article available to read on EtoBox.

What is Sharp estimates for the Cram\'{e}r transform of log-concave measures and geometric applications about?

We establish a new comparison between the Legendre transform of the cumulant generating function and the half-space depth of an arbitrary log-concave probability distribution on the real line, that carries on to the multidimensional setting. Combined with sharp estimates for the Cram\'{e}r transform of rotationally invariant measures, we are led to some new phase-transition type results for the asymptotics of the expected measure of random polytopes. As a byproduct of our analysis, we address a question on the sharp exponential separability constant for log-concave distributions, in the symmetric case.

Author

Brazitikos, Silouanos; Chasapis, Giorgos

Published

2024

Language

EN