标题： KPZ固定点 显示英文标题

标题： The KPZ fixed point

摘要： 对于具有任意右有限初始条件的完全不对称简单排斥过程（TASEP）的高度函数的多点分布，推导出了一个显式的弗雷德霍姆行列式公式。该方法是通过求解[Sas05; BFPS07]中发现的双正交系/非交叉路径表示。所得的核涉及一个被强制击中由初始数据定义的曲线的随机游走的转移概率。在KPZ 1:2:3标度极限下，该公式以清晰的方式导致了一个弗雷德霍姆行列式公式，该公式以基于布朗运动的类似核来表示KPZ universality 类中心的标度不变马尔可夫过程的转移概率。该公式可以直接再现已知的特殊自相似解，例如Airy$_1$和Airy$_2$过程。该过程取值于局部看起来像布朗运动的实值函数，并且在时间上是Holder$1/3-$的。KPZ固定点和TASEP都被证明是在某种意义上是随机可积系统，因为它们的转移概率的时间演化可以通过一种新的布朗散射变换及其离散模拟线性化。 显示英文摘要

摘要： An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary right-finite initial condition. The method is by solving the biorthogonal ensemble/non-intersecting path representation found by [Sas05; BFPS07]. The resulting kernel involves transition probabilities of a random walk forced to hit a curve defined by the initial data. In the KPZ 1:2:3 scaling limit the formula leads in a transparent way to a Fredholm determinant formula, in terms of analogous kernels based on Brownian motion, for the transition probabilities of the scaling invariant Markov process at the centre of the KPZ universality class. The formula readily reproduces known special self-similar solutions such as the Airy$_1$ and Airy$_2$ processes. The process takes values in real valued functions which look locally like Brownian motion, and is H\"older $1/3-$ in time. Both the KPZ fixed point and TASEP are shown to be stochastic integrable systems in the sense that the time evolution of their transition probabilities can be linearized through a new Brownian scattering transform and its discrete analogue.