Transport-majorization to analytic and geometric inequalities
arXiv:2110.03641 · doi:10.1016/j.jfa.2022.109717
Abstract
We introduce a transport-majorization argument that establishes a majorization in the convex order between two densities, based on control of the gradient of a transportation map between them. As applications, we give elementary derivations of some delicate Fourier analytic inequalities, which in turn yield geometric "slicing-inequalities" in both continuous and discrete settings. As a further consequence of our investigation we prove that any strongly log-concave probability density majorizes the Gaussian density and thus the Gaussian density maximizes the Rényi and Tsallis entropies of all orders among all strongly log-concave densities.
arXiv comment26 pages, online at Journal of Functional Analysis
References in corpus (7)
- Rényi Divergence and Kullback-Leibler Divergence
- On A Mixture Of Brenier and Strassen Theorems
- The optimal constants in Khintchine's inequality for the case 2<p<3
- Bernoulli sums and Rényi entropy inequalities
- Hyperplane Sections of Cylinders
- A proof of the Caffarelli contraction theorem via entropic regularization
- Majorization revisited: Comparison of norms in interpolation scales