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An Information-Theoretic Proof of the Kac--Bernstein Theorem (2202.06005v2)
Published 12 Feb 2022 in cs.IT, math.IT, and math.PR
Abstract: A short, information-theoretic proof of the Kac--Bernstein theorem, which is stated as follows, is presented: For any independent random variables $X$ and $Y$, if $X+Y$ and $X-Y$ are independent, then $X$ and $Y$ are normally distributed.