论文标题
通过非电向随机步行的随机散型砖的高度波动
Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks
论文作者
论文摘要
在本文中，我们研究了三角形晶格上多边形域随机侧侧斜线的高度波动，这是通过非电向的Bernoulli随机步行的高度波动。对于一大批具有一个水平上限边缘的多边形，我们表明这些随机高度功能会像Kenyon和Okounkov [28]所预测的那样收敛到高斯自由场。我们证明的关键要素是Borodin，Guionnet和Gorin [5]引入的离散循环方程式的动态版本，这可能具有独立的兴趣。
In this paper we study height fluctuations of random lozenge tilings of polygonal domains on the triangular lattice through nonintersecting Bernoulli random walks. For a large class of polygons which have exactly one horizontal upper boundary edge, we show that these random height functions converge to a Gaussian Free Field as predicted by Kenyon and Okounkov [28]. A key ingredient of our proof is a dynamical version of the discrete loop equations as introduced by Borodin, Guionnet and Gorin [5], which might be of independent interest.
