Journal
JOURNAL OF THEORETICAL PROBABILITY
Volume 13, Issue 3, Pages 843-857Publisher
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/A:1007818830500
Keywords
entropy; compact groups; convolution
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We investigate the behaviour of the entropy of convolutions of independent random variables on compact groups. We provide an explicit exponential bound on the rate of convergence of entropy to its maximum. Equivalently, this proves convergence of the density to uniformity, in the sense of Kullback-Leibler. We prove that this convergence lies strictly between uniform convergence of densities (as investigated by Shlosman and Major), and weak convergence (the sense of the classical Ito-Kawada theorem). In fact it lies between convergence in L1+epsilon and convergence in L-1.
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