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

4 Scopus citations

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 (US)
Title of host publication	2017 IEEE International Symposium on Information Theory, ISIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	898-902
Number of pages	5
ISBN (Electronic)	9781509040964
DOIs	https://doi.org/10.1109/ISIT.2017.8006658
State	Published - Aug 9 2017
Externally published	Yes
Event	2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8095

Other

Other	2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/Territory	Germany
City	Aachen
Period	6/25/17 → 6/30/17

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.2017.8006658

Cite this

A de Bruijn identity for discrete random variables. / Johnson, Oliver; Guha, Saikat.
2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 898-902 8006658 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Johnson, O & Guha, S 2017, A de Bruijn identity for discrete random variables. in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8006658, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 898-902, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 6/25/17. https://doi.org/10.1109/ISIT.2017.8006658

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A de Bruijn identity for discrete random variables

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