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arXiv · 1701.02228

A Proof of the Herschel-Maxwell Theorem Using the Strong Law of Large Numbers

Somabha Mukherjee
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Abstract

In this article, we use the strong law of large numbers to give a proof of the Herschel-Maxwell theorem, which characterizes the normal distribution as the distribution of the components of a spherically symmetric random vector, provided they are independent. We present shorter proofs under additional moment assumptions, and include a remark, which leads to another strikingly short proof of Maxwell's characterization using the central limit theorem.

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Somabha Mukherjee. 2017-01-03. A Proof of the Herschel-Maxwell Theorem Using the Strong Law of Large Numbers. https://arxiv.org/abs/1701.02228

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