论文标题
流浪者，KPZ波动和Tracy的变形 - Widom Goe分布的通风过程
Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
论文作者
论文摘要
我们使用$ m $ wanderers研究了抛物线的高级过程的上限分布，或者等同于$ n $ n $ n $ no-n $ brownian bridges的最大高度的极限，即$ n \ to \ infty $，在第一个$ n-m $的情况下，在第一个$ n-m $中开始，并在原点开始，并在原点和$ m $ $ $ $ $ $ $ $之间。该分布提供了Tracy-Widom Goe分布的200万美元参数变形，该分配以对应于所有Brownian Paths的限制恢复。 我们提供了此分布函数的几个描述：（i）弗雷德姆决定因素公式； （ii）在PainlevéII功能方面的公式； （iii）作为KPZ固定点的边缘的表示形式，其初始数据作为固定系统反射的布朗尼运动的固定系统的最高路径； （iv）作为Bloemendal-virag PDE版本的解决方案（Arxiv：1011.1877，Arxiv：1109.3704），用于尖刺的Tracy-widom分布； （v）表示作为KDV方程的解。我们还与边界源的最后一段渗透模型讨论了连接。
We study the distribution of the supremum of the Airy process with $m$ wanderers minus a parabola, or equivalently the limit of the rescaled maximal height of a system of $N$ non-intersecting Brownian bridges as $N\to\infty$, where the first $N-m$ paths start and end at the origin and the remaining $m$ go between arbitrary positions. The distribution provides a $2m$-parameter deformation of the Tracy--Widom GOE distribution, which is recovered in the limit corresponding to all Brownian paths starting and ending at the origin. We provide several descriptions of this distribution function: (i) A Fredholm determinant formula; (ii) A formula in terms of Painlevé II functions; (iii) A representation as a marginal of the KPZ fixed point with initial data given as the top path in a stationary system of reflected Brownian motions with drift; (iv) A characterization as the solution of a version of the Bloemendal--Virag PDE (arXiv:1011.1877, arXiv:1109.3704) for spiked Tracy--Widom distributions; (v) A representation as a solution of the KdV equation. We also discuss connections with a model of last passage percolation with boundary sources.
