Work

The John inclusion for log-concave functions

Year: 2026

Type: article

Abstract: John's inclusion states that a convex body in R d can be covered by the d -dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-concave functions. As a byproduct of our approach, we establish the following asymptotically tight inequality: For any log-concave function f with finite, positive integral, there exist a positive definite matrix A , a point a ∈ R d , and a positive constant α such that χ B d ( x ) ≤ α f ( A ( x − a ) ) ≤ d + 1 ⋅ e − | x | d + 2 + ( d + 1 ) , where χ B d is the indicator function of the unit ball B d .

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2026.130441

Author: Grigory Ivanov

Institution: Pontifícia Universidade Católica do Rio de Janeiro

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior