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Two remarks on generalized entropy power inequalities (1904.02314v1)
Published 4 Apr 2019 in cs.IT, math.IT, and math.PR
Abstract: This note contributes to the understanding of generalized entropy power inequalities. Our main goal is to construct a counter-example regarding monotonicity and entropy comparison of weighted sums of independent identically distributed log-concave random variables. We also present a complex analogue of a recent dependent entropy power inequality of Hao and Jog, and give a very simple proof.