A notion of entropy on the roots of polynomials

Aurelien Gribinski

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arXiv · 1907.12826

A notion of entropy on the roots of polynomials

Aurelien Gribinski

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Abstract

We introduce a canonical notion of entropy for polynomials analogue to that of random variables in probability. We prove that entropy increases smoothly with respect to finite free addition. In particular we get the new inequality : $ \Dis(p-tp')>\Dis(p) $ for a polynomial $p$, its derivative $p'$ and t any non zero real.

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BibTeX RIS

Aurelien Gribinski. 2023-11-06. A notion of entropy on the roots of polynomials. https://arxiv.org/abs/1907.12826

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