An information-theoretic proof of Nash's inequality [PDF]
Giuseppe ToscaniWe 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 an improved Nash's inequality with the sharp constant.View original: http://arxiv.org/abs/1206.2130
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