论文标题
KPZ固定点的有条件缩放限制，高度在一个位置倾向于无穷大
A conditional scaling limit of the KPZ fixed point with height tending to infinity at one location
论文作者
论文摘要
我们考虑KPZ固定点$ \ {\ MATHSF H（X，T）\} _ {X \ in \ Mathbb R，T> 0} $在$ \ Mathsf H（0，T）= L as $ l $的条件下。主要结果是在线段附近的$ \ Mathsf H $波动的有条件限制定理，该区域连接了台阶和平坦初始条件的线段连接原点$（0,0）$（0,0）$（0,0）$（0，T）$。极限随机场可以表示为两个独立的布朗桥的功能，此外，极限随机场也取决于KPZ固定点的初始定律。特别是对于时间波动，在$（0,0）$和$（0，t）$之间按线段索引的限制过程，当KPZ具有步骤初始条件时，具有两个独立的布朗尼桥的定律；当KPZ具有平坦的初始条件时，极限过程的定律为两个独立的布朗尼桥，另外每个桥都受到公共高斯随机变量的扰动。对于时空的波动，条件限制定理揭示了针对定向景观的点对点大地测量的渐近行为，该景观是根据其长度和长度趋向于无穷大的。
We consider the asymptotic behavior of the KPZ fixed point $\{\mathsf H(x,t)\}_{x\in\mathbb R, t>0}$ conditioned on $\mathsf H(0,T)=L$ as $L$ goes to infinity. The main result is a conditional limit theorem for the fluctuations of $\mathsf H$ in the region near the line segment connecting the origin $(0,0)$ and $(0,T)$ for both step and flat initial conditions. The limit random field can be represented as a functional of two independent Brownian bridges, and in addition the limit random field depends also on the initial law of the KPZ fixed point. In particular for temporal fluctuations, the limit process indexed by line segment between $(0,0)$ and $(0,T)$, when the KPZ is with step initial condition, has the law of the minimum of two independent Brownian bridges; and when the KPZ is with flat initial condition the limit process has the law of the minimum of two independent Brownian bridges, each in addition perturbed by a common Gaussian random variable. For spatial-temporal fluctuations, the conditional limit theorem sheds light on the asymptotic behaviors of the point-to-point geodesic of the directed landscape conditioned on its length and as the length tends to infinity.
