arXiv subjects
Publications and source records attributed to Joseph Lehec.
We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell's formula for the Laplace transform. As an application, we give unified and short proofs of a number of functional inequalities.
We give a proof based on the Poincaré inequality of the symmetric property tau for the Gaussian measure. This property turns out to be equivalent to a certain functional form of the Blaschke-Santaló inequality, as explained in a paper by Artstein, Klartag and Milman.
This paper deals with Latała's estimation of the moments of Gaussian chaoses. It is shown that his argument can be simplified significantly using Talagrand's generic chaining.
We give a direct proof of a functional Santalo inequality due to Fradelizi and Meyer. This provides a new proof of the Blaschke-Santalo inequality. The argument combines a logarithmic form of the Prekopa-Leindler inequality and a partition theorem of Yao and Yao.
The Yao-Yao partition theorem states that given a probability measure on an affine space of dimension n having a density which is continuous and bounded away from 0, it is possible to partition the space into 2^n regions of equal measure in such a way that every affine hyperplane avoids at least one of the regions. We give a constructive proof of this result and extend it to slightly more general measures.
We give a simple proof of a functional version of the Blaschke-Santalo inequality due to Artstein, Klartag and Milman. The proof is by induction on the dimension and does not use the Blaschke-Santalo inequality.