A de Bruijn identity for discrete random variables

Oliver Johnson; Saikat Guha

doi:10.1109/ISIT.2017.8006658

A de Bruijn identity for discrete random variables

Oliver Johnson, Saikat Guha

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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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.

Original language	English
Title of host publication	2017 IEEE International Symposium on Information Theory (ISIT 2017)
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	898-902
Number of pages	5
ISBN (Electronic)	9781509040964
ISBN (Print)	9781509040971
DOIs	https://doi.org/10.1109/ISIT.2017.8006658
Publication status	Published - Aug 2017

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ISSN (Print)	2157-8117

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10.1109/ISIT.2017.8006658

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title = "A de Bruijn identity for discrete random variables",

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.",

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AB - 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.

UR - https://arxiv.org/abs/1701.07089

U2 - 10.1109/ISIT.2017.8006658

DO - 10.1109/ISIT.2017.8006658

M3 - Conference Contribution (Conference Proceeding)

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BT - 2017 IEEE International Symposium on Information Theory (ISIT 2017)

PB - Institute of Electrical and Electronics Engineers (IEEE)

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A de Bruijn identity for discrete random variables

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A de Bruijn identity for discrete random variables

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