论文标题
非亚伯相关性不平等和稳定的决定性多项式
Non-Abelian correlation inequalities and stable determinantal polynomials
论文作者
论文摘要
我们考虑$ O（n）$和$ \ Mathbb {C} \ Mathbb {p}^{n-1} $模型的不变性可观察到的相关性，即相对于自然组合群体，零耦合的模型。在一个掌握集成剂的极限的极限中，我们表明这些相关性成为基尔chhoff多项式的逆力。因此，后者提供了一个简化的玩具模型，以研究相关产品之间的不平等现象。诸如自旋模型相关性的铁磁行为之类的属性在此渐近极限中与对数硫型二极管性相对应，这是Kirchhoff多项式的雷利特性的结果。除了上述严格的渐近造物外，本文的主要结果是一般定理，该定理表明，某些决定性稳定多项式的逆半数势力，例如Kirchhoff多项式，满足GKS 2不平等现象的概括和胆小鬼的不平等现象。我们以一些开放的问题为首，例如，最后一个陈述是否存在于不是半智商的权力的问题。这导致了Scott和Sokal最近调查的完整单调性属性的Hirota-BiLinear类似物。
We consider the correlations of invariant observables for the $O(N)$ and $\mathbb{C}\mathbb{P}^{N-1}$ models at zero coupling, namely, with respect to the natural group-invariant measure. In the limit where one takes a large power of the integrand, we show that these correlations become inverse powers of the Kirchhoff polynomial. The latter therefore provide a simplified toy model for the investigation of inequalities between products of correlations. Properties such as ferromagnetic behavior for spin model correlations correspond, in this asymptotic limit, to log-ultramodularity which is a consequence of the Rayleigh property of the Kirchhoff polynomial. In addition to the above rigorous asymptotics, the main result of this article is a general theorem which shows that inverse half-integer powers of certain determinantal stable polynomials, such as the Kirchhoff polynomials, satisfy generalizations of the GKS 2 inequalities and the Ginibre inequalities. We conclude with some open problems, e.g., the question of whether the last statement holds for powers which are not half-integers. This leads to a Hirota-bilinear analogue of the complete monotonicity property recently investigated by Scott and Sokal.
