Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions
Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions
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DOI：
10.1016/j.jfa.2018.12.008
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发表时间：
2017-10
影响因子：
1.7
通讯作者：
E. Dimitrov;Alisa Knizel
中科院分区：
文献类型：
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作者：
E. Dimitrov;Alisa Knizel
我们研究了（移位）二次格上的一般类对数气体系综。我们证明了相应的经验措施，满足大数定律，其全球波动是高斯与一个普遍的协方差。我们应用我们的一般结果分析了由Borodin，Gorin和Rains引入的aq-boxed平面分割模型的渐近性态。特别地，我们证明了在一个固定的切片上的高度函数的全局波动是由二维高斯自由场的拉回的一维部分描述的，我们的方法是基于源于Nekrasov和他的合作者的工作的Schwinger-Dyson（或回路）方程的aq-模拟，并将Borodin，Gorin和Guionnet开发的方法扩展到二次晶格。
We study a general class of log-gas ensembles on (shifted) quadratic lattices. We prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are Gaussian with a universal covariance. We apply our general results to analyze the asymptotic behavior of aq-boxed plane partition model introduced by Borodin, Gorin and Rains. In particular, we show that the global fluctuations of the height function on a fixed slice are described by a one-dimensional section of a pullback of the two-dimensional Gaussian free field.Our approach is based on aq-analogue of the Schwinger–Dyson (or loop) equations, which originate in the work of Nekrasov and his collaborators, and extends the methods developed by Borodin, Gorin and Guionnet to quadratic lattices.