An information-theoretic proof of Nash's inequality
Information Theory
2012-07-13 v2 Mathematical Physics
Functional Analysis
math.IT
math.MP
Abstract
We show that an information-theoretic property of Shannon's entropy power, known as concavity of entropy power, can be fruitfully employed to prove inequalities in sharp form. In particular, the concavity of entropy power implies the logarithmic Sobolev inequality, and Nash's inequality with the sharp constant.
Cite
@article{arxiv.1206.2130,
title = {An information-theoretic proof of Nash's inequality},
author = {Giuseppe Toscani},
journal= {arXiv preprint arXiv:1206.2130},
year = {2012}
}