An information-theoretic proof of Nash%26apos;s inequality

作者：Toscani Giuseppe^*

来源：Rendiconti Lincei. Matematica e Applicazioni, 2013, 24(1): 83-93.

DOI：10.4171/RLM/645

• Entropy power
• Fisher information
• logarithmic Sobolev inequality
• Nash%26apos
• s inequality

We show that an information-theoretic property of Shannon%26apos;s entropy power, known as concavity of entropy power [7], can be fruitfully employed to prove inequalities in sharp form. In particular, the concavity of entropy power implies the logarithmic Sobolev inequality, and the Nash%26apos;s inequality with the sharp constant.

• 出版日期2013