English

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

Information Theory 2022-02-22 v2 math.IT Probability

Abstract

A short, information-theoretic proof of the Kac--Bernstein theorem, which is stated as follows, is presented: For any independent random variables XX and YY, if X+YX+Y and XYX-Y are independent, then XX and YY are normally distributed.

Keywords

Cite

@article{arxiv.2202.06005,
  title  = {An Information-Theoretic Proof of the Kac--Bernstein Theorem},
  author = {J. Jon Ryu and Young-Han Kim},
  journal= {arXiv preprint arXiv:2202.06005},
  year   = {2022}
}

Comments

4 pages