Work

Sharp estimates for the Cramér transform of log-concave measures and geometric applications

Year: 2025

Type: article

Abstract: 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 Cramér 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.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2025.110407

Authors: Silouanos Brazitikos, Giorgos Chasapis

Institutions: University of Crete, University of Ioannina

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: European Commission, Hellenic Foundation for Research and Innovation