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2 votes
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Reverse Pinsker's inequality for smooth density classes

The answer is no. E.g., suppose that both $f$ and $g$ are supported on $B=[0,1]$, with $f=1$ on $B$ and $$g(x)=(1-h+x)\,1(0\le x<h)+1(h\le x<1-h)+(x+h)\,1(1-h\le x\le1)$$ for $h\in(0,1/2)$ and $...
Iosif Pinelis's user avatar
1 vote

Are the derivatives of the differential entropy power alternating?

Michel Ledoux discusses this as the "completely monotone conjecture" in his paper Differentials of entropy and Fisher information along heat flow: a brief review of some conjectures
Fabrice Baudoin's user avatar

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