零点、混沌比与独立多项式逼近的计算复杂性
Zeros, chaotic ratios and the computational complexity of approximating the independence polynomial
摘要：
独立多项式起源于统计物理学，作为核心模型的分拆函数。多项式的复零点的位置与相变有关，并且在设计有效的算法来近似计算多项式的评估中起着重要的作用。本文将独立多项式复零点的位置直接与独立多项式逼近估计的计算难度联系起来。我们这样做，而且有关的零点的位置，一个自然相关联的家庭的有理函数的混沌行为，占领率。
英文摘要：
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.
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