The oriented swap process and last passage percolation
The oriented swap process and last passage percolation
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DOI：
10.1002/rsa.21055
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发表时间：
2020-05
影响因子：
1
通讯作者：
E. Bisi;F. D. Cunden;Shane Gibbons;D. Romik
中科院分区：
文献类型：
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作者：
E. Bisi;F. D. Cunden;Shane Gibbons;D. Romik
我们提出了新的概率和组合身份有关的三个随机过程：定向交换过程（OSP）的n粒子，角生长过程，和最后一次通过渗流（LPP）模型。我们证明了一个概率的身份，有关的随机向量的LPP倍，其对偶，使用的Robinson-Schensted-Knuth和Burge之间的对偶对应。将这两个向量与OSP中的“最后交换时间”的向量相关联的第二个概率恒等式是概率恒等式。我们首先将这个恒等式重新表述为一个纯粹的组合恒等式，然后给出了这个恒等式的计算机辅助证明，并讨论了它与Edelman-Greene对应的关系。该恒等式对OSP的吸收时间分布提供了精确的有限n和渐近预测，从而有条件地解决了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 (OSP) on n particles, the corner growth process, and the last passage percolation (LPP) model. We prove one of the probabilistic identities, relating a random vector of LPP 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 OSP, is conjectural. We give a computer‐assisted proof of this identity for n≤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 OSP, thus conditionally solving an open problem posed by Angel, Holroyd, and Romik.