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Entropy jumps in the presence of a spectral gap. (English) Zbl 1036.94003

Let \(X\) be a random variable whose density satisfies a Poincaré inequality and \(Y\) be an independent copy of \(X\). The authors show that the entropy of \((X + Y)/\sqrt 2\) is greater than that of \(X\) by a fixed fraction of the entropy gap between \(X\) and the Gaussian with the same variance.

MSC:

94A17 Measures of information, entropy
60F05 Central limit and other weak theorems

Keywords:

entropy gap
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