Entropy versions of additive inequalities

09/27/2018

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by   Alberto Espuny Díaz, et al.

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The connection between inequalities in additive combinatorics and analogous versions in terms of the entropy of random variables has been extensively explored over the past few years. This paper extends a device introduced by Ruzsa in his seminal work introducing this correspondence. This extension provides a toolbox for establishing the equivalence between sumset inequalities and their entropic versions. It supplies simpler proofs of known results and opens a path for obtaining new ones. Some new examples in nonabelian groups illustrate the power of the device.