Emergent Mind
An information-theoretic proof of Nash's inequality
(1206.2130)
Published Jun 11, 2012
in
cs.IT
,
math-ph
,
math.FA
,
math.IT
,
and
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.
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