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On the rate of convergence in the entropic central limit theorem. (English) Zbl 1055.94004
The authors study the rate at which entropy is produced by linear combinations of independent random variables which satisfy a spectral gap condition. This is done by considering a reduction to an inequality for Fisher information and using variational representations of it. Then techniques are used to produce an optimal test function.

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