论文标题
最后一段渗透和定向聚合物的隐藏不变性
Hidden invariance of last passage percolation and directed polymers
论文作者
论文摘要
$ \ Mathbb z^2 $上的最后一段段落和指示聚合物模型在翻译和某些反射下是不变的。当这些模型具有来自RSK对应关系或几何RSK对应关系的可集成结构时（例如几何最后一段渗透或log-gamma聚合物）时，我们表明这些基本的敌人可以与解耦合结合，以产生丰富的新符号集。除其他结果外，我们证明了上一次通道时间，地球位置，差异概率，聚合物分区功能和淬火聚合物测量的移位和重新排列不变性陈述。我们还使用我们的框架来找到经典RSK对应的“炒”版本，并找到月球多元群落的RSK对应。结果扩展到限制模型，包括KPZ方程和通风板。
Last passage percolation and directed polymer models on $\mathbb Z^2$ are invariant under translation and certain reflections. When these models have an integrable structure coming from either the RSK correspondence or the geometric RSK correspondence (e.g. geometric last passage percolation or the log-gamma polymer), we show that these basic invariances can be combined with a decoupling property to yield a rich new set of symmetries. Among other results, we prove shift and rearrangement invariance statements for last passage times, geodesic locations, disjointness probabilities, polymer partition functions, and quenched polymer measures. We also use our framework to find `scrambled' versions of the classical RSK correspondence, and to find an RSK correspondence for moon polyominoes. The results extend to limiting models, including the KPZ equation and the Airy sheet.
