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Zeros, chaotic ratios and the computational complexity of approximating the independence polynomial
Published online by Cambridge University Press: 24 November 2023
Abstract
The independence polynomial originates in statistical physics as the partition function of the hard-core model. The location of the complex zeros of the polynomial is related to phase transitions, and plays an important role in the design of efficient algorithms to approximately compute evaluations of the polynomial.
In this paper we directly relate the location of the complex zeros of the independence polynomial to computational hardness of approximating evaluations of the independence polynomial. We do this by moreover relating the location of zeros to chaotic behaviour of a naturally associated family of rational functions; the occupation ratios.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 176 , Issue 2 , March 2024 , pp. 459 - 494
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society