论文标题
定向交换过程和最后一个通过
The oriented swap process and last passage percolation
论文作者
论文摘要
我们提出了有关三个随机过程的新概率和组合身份：$ n $粒子上的定向交换过程，角落增长过程以及最后一个段落渗透模型。我们证明了概率的身份之一，将最后一段渗透时间的随机向量与二元相关，使用了Robinson-Schensted-Knuth和Burge对应关系之间的双重性。在定向交换过程中，将这两个向量与“最后交换时间”向量相关的第二个概率身份是猜想的。在首先将其作为纯粹的组合身份重新定义后，我们为$ n \ le 6 $提供了计算机辅助证明，并讨论了它与Edelman-Greene通信的关系。猜想的身份提供了有关定向交换过程吸收时间的分布的精确有限$ n $和渐近预测，因此有条件地解决了Angel，Holroyd和Romik提出的开放问题。
We present new probabilistic and combinatorial identities relating three random processes: the oriented swap process on $n$ particles, the corner growth process, and the last passage percolation model. We prove one of the probabilistic identities, relating a random vector of last passage percolation times to its dual, using the duality between the Robinson-Schensted-Knuth and Burge correspondences. A second probabilistic identity, relating those two vectors to a vector of 'last swap times' in the oriented swap process, is conjectural. We give a computer-assisted proof of this identity for $n\le 6$ after first reformulating it as a purely combinatorial identity, and discuss its relation to the Edelman-Greene correspondence. The conjectural identity provides precise finite-$n$ and asymptotic predictions on the distribution of the absorbing time of the oriented swap process, thus conditionally solving an open problem posed by Angel, Holroyd and Romik.
