论文标题
单方面反射的布朗运动和KPZ固定点
One-sided reflected Brownian motions and the KPZ fixed point
论文作者
论文摘要
我们考虑了单方面反射的布朗尼运动的系统，该系统与Brownian的最后一段渗透相同。 We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of exponential random walks, and that it converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling invariant Markov process defined in [MQR17] and believed to govern the long time large scale fluctuations for all models in the KPZ universality class.最近在[DOV18]中显示了Brownian的最后一个通道渗透，以收敛到通风板（或定向景观），该纸张定义为通风线集合的功能的强限制。这建立了KPZ固定点的变异公式。
We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of exponential random walks, and that it converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling invariant Markov process defined in [MQR17] and believed to govern the long time large scale fluctuations for all models in the KPZ universality class. Brownian last passage percolation was shown recently in [DOV18] to converge to the Airy sheet (or directed landscape), defined there as a strong limit of a functional of the Airy line ensemble. This establishes the variational formula for the KPZ fixed point in terms of the Airy sheet.
