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Propagation of Localization Optimal Entropy Production and Convergence rates for the Central Limit Theorem

222   0   0.0 ( 0 )
 Added by Avy Soffer
 Publication date 2011
  fields Physics
and research's language is English




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We prove for the rescaled convolution map $fto fcircledast f$ propagation of polynomial, exponential and gaussian localization. The gaussian localization is then used to prove an optimal bound on the rate of entropy production by this map. As an application we prove the convergence of the CLT to be at the optimal rate $1/sqrt{n}$ in the entropy (and $L^1$) sense, for distributions with finite 4th moment.



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