A de Bruijn identity for discrete random variables
Information Theory
2017-08-22 v1 math.IT
Probability
Quantum Physics
Abstract
We discuss properties of the "beamsplitter addition" operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.
Cite
@article{arxiv.1701.07089,
title = {A de Bruijn identity for discrete random variables},
author = {Oliver Johnson and Saikat Guha},
journal= {arXiv preprint arXiv:1701.07089},
year = {2017}
}
Comments
9 pages, shorter version submitted to ISIT 2017