不相交道路、随机拼接与随机矩阵
Non-intersecting Paths, Random Tilings and Random Matrices
摘要：
我们调查了某些措施引起的家庭的非相交路径的多米诺骨牌平铺的阿兹特克钻石，菱形平铺的ABC-六边形，二聚体模型的圆柱形砖格和增长模型。所获得的措施，例如Krawtchouk和哈恩合奏，具有相同的结构作为随机矩阵理论中的特征值措施，如GUE，这实际上可以从非相交的布朗运动。测量的推导基于Karlin-McGregor或Lindström-Gessel-Viennot方法。我们使用的措施，以显示一些渐近结果的模型。
英文摘要：
We investigate certain measures induced by families of non-intersecting paths in domino tilings of the Aztec diamond, rhombus tilings of an abc-hexagon, a dimer model on a cylindrical brick lattice and a growth model. The measures obtained, e.g. the Krawtchouk and Hahn ensembles, have the same structure as the eigenvalue measures in random matrix theory like GUE, which can in fact be obtained from non-intersecting Brownian motions. The derivations of the measures are based on the Karlin-McGregor or Lindström-Gessel-Viennot method. We use the measure to show some asymptotic results for the models.
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