A de Bruijn identity for discrete random variables

Oliver Johnson, Saikat Guha

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

4 Citations (Scopus)
286 Downloads (Pure)


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 languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory (ISIT 2017)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages5
ISBN (Electronic)9781509040964
ISBN (Print)9781509040971
Publication statusPublished - Aug 2017

Publication series

ISSN (Print)2157-8117


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