Pub Date : 2024-10-25DOI: 10.1109/TIT.2024.3477754
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Pub Date : 2024-10-25DOI: 10.1109/TIT.2024.3477756
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Pub Date : 2024-09-25DOI: 10.1109/TIT.2024.3466566
Paul Mansanarez;Guillaume Poly;Yvik Swan
We investigate the properties of the entropy of a probability measure along the heat flow and more precisely we seek for closed algebraic representations of its derivatives. Provided that the measure admits moments of any order, it has been proved in Guo et al. (2010) that this functional is smooth, and in Ledoux (2016) that its derivatives at zero can be expressed into multivariate polynomials evaluated in the moments (or cumulants) of the underlying measure. Moreover, these algebraic expressions are derived through $Gamma $