Six-vertex models and the GUE-corners process
Six-vertex models and the GUE-corners process
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六顶点模型和 GUE 角过程
DOI：
10.1093/imrn/rny072
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
E. Dimitrov
中科院分区：
文献类型：
--
作者：
E. Dimitrov
本文从统计力学的角度考虑了六点模型上的一类概率分布，它起源于https://arxiv.org/abs/1601.05770.的高自旋点模型我们在麦克唐纳差运算符的启发下定义了运算符，这些运算符提取各种关联函数，测量观察到不同箭头配置的概率。我们的算子的发展在很大程度上是基于一族引人注目的对称有理函数族的性质，这些性质以前在https://arxiv.org/abs/1410.0976.中进行了研究
对于我们考虑的这类模型，相关函数可以用多个轮廓积分来表示，这适合于渐近分析。对于特定的参数选择，我们通过最速下降法分析了相关函数的极限。结合Gelfand-Tsetlin锥和图样上关于Gibbs测度的一些新结果，我们证明了我们的六顶点模型在边界附近的渐近行为是由格角点过程描述的。
In this paper we consider a class of probability distributions on the six-vertex model from statistical mechanics, which originate from the higher spin vertex models of https://arxiv.org/abs/1601.05770. We define operators, inspired by the Macdonald difference operators, which extract various correlation functions, measuring the probability of observing different arrow configurations. The development of our operators is largely based on the properties of a remarkable family of symmetric rational functions, which were previously studied in https://arxiv.org/abs/1410.0976.
For the class of models we consider, the correlation functions can be expressed in terms of multiple contour integrals, which are suitable for asymptotic analysis. For a particular choice of parameters we analyze the limit of the correlation functions through a steepest descent method. Combining this asymptotic statement with some new results about Gibbs measures on Gelfand-Tsetlin cones and patterns, we show that the asymptotic behavior of our six-vertex model near the boundary is described by the GUE-corners process.
影响因子：
3
作者：
Borodin, Alexei;Corwin, Ivan;Ferrari, Patrik
通讯作者：
Ferrari, Patrik