Groves的一个北极圈定理
An arctic circle theorem for groves
摘要：
在早期的工作中，Jockusch，Propp和Shor证明了一个定理，该定理描述了阿兹特克钻石随机镶嵌的均匀瓷砖角落与该地区内部更不可预测的“温带”之间边界的极限形状。所谓的北极圈定理精确地解释了在阿兹特克大钻石随机镶嵌中观察到的现象。在这里，我们研究一个相关的组合模型称为格罗夫。创建卡罗尔和施派尔作为组合解释劳伦多项式的立方递归，格罗夫有可观察到的冻结区域，我们精确地描述通过渐近分析的生成函数。我们的方法还提供了另一种方法来证明阿兹特克钻石的北极圈定理。
英文摘要：
In earlier work, Jockusch, Propp, and Shor proved a theorem describing the limiting shape of the boundary between the uniformly tiled corners of a random tiling of an Aztec diamond and the more unpredictable `temperate zone' in the interior of the region. The so-called arctic circle theorem made precise a phenomenon observed in random tilings of large Aztec diamonds. Here we examine a related combinatorial model called groves. Created by Carroll and Speyer as combinatorial interpretations for Laurent polynomials given by the cube recurrence, groves have observable frozen regions which we describe precisely via asymptotic analysis of a generating function. Our approach also provides another way to prove the arctic circle theorem for Aztec diamonds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
