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A de Bruijn identity for discrete random variables (1701.07089v1)
Published 23 Jan 2017 in cs.IT, math.IT, math.PR, and quant-ph
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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