Real Stability and Log Concavity are coNP-Hard

Tracy Chin

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arXiv · 2405.00162

Real Stability and Log Concavity are coNP-Hard

Tracy Chin

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Abstract

Real-stable, Lorentzian, and log-concave polynomials are well-studied classes of polynomials, and have been powerful tools in resolving several conjectures. We show that the problems of deciding whether a polynomial of fixed degree is real stable or log concave are coNP-hard. On the other hand, while all homogeneous real-stable polynomials are Lorentzian and all Lorentzian polynomials are log concave on the positive orthant, the problem of deciding whether a polynomial of fixed degree is Lorentzian can be solved in polynomial time.

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Tracy Chin. 2024-04-30. Real Stability and Log Concavity are coNP-Hard. https://arxiv.org/abs/2405.00162

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