An Information-Theoretic Proof of the Kac--Bernstein Theorem

2022/02/12 by Ryu, J. Jon, Kim, Young-Han
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2202.06005

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.

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