Real Stability and Log Concavity are coNP-Hard
<|reference_start|>Real Stability and Log Concavity are coNP-Hard: 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.<|reference_end|>
@article{chin2024real,
    title={Real Stability and Log Concavity are coNP-Hard},
    author={Tracy Chin},
    journal={arXiv preprint arXiv:2405.00162},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.00162},
    primaryClass={math.OC cs.CC math.CO}
}