论文标题
关于布朗聚合物的限制性定律，带有几何区域倾斜
On the limiting law of line ensembles of Brownian polymers with geometric area tilts
论文作者
论文摘要
我们研究了坚硬的壁上的非交叉布朗桥的线团，每个桥都被其下方区域的区域倾斜，并具有几何生长的前成分。该模型模仿了硬墙上方的$（2+1）$ D SOS模型的水平线，并由Caputo，Ioffe和Wachtel在2019年的两幅作品中进行了研究。在这些作品中，对于任何固定的$ k $，在零或自由边界条件下建立了最高$ k $路径的法律的紧密度，在前一种环境中，这意味着通过单调性参数存在限制。在这里，我们解决了在自由边界条件下限制的开放问题：我们证明，作为间隔长度，随后是路径数，转到$ \ infty $，Top $ k $路径汇聚到与自由边界情况相同的限制，如Caputo，Ioffe，Ioffe和Wachtel的猜想。
We study the line ensembles of non-crossing Brownian bridges above a hard wall, each tilted by the area of the region below it with geometrically growing pre-factors. This model, which mimics the level lines of the $(2+1)$D SOS model above a hard wall, was studied in two works from 2019 by Caputo, Ioffe and Wachtel. In those works, the tightness of the law of the top $k$ paths, for any fixed $k$, was established under either zero or free boundary conditions, which in the former setting implied the existence of a limit via a monotonicity argument. Here we address the open problem of a limit under free boundary conditions: we prove that as the interval length, followed by the number of paths, go to $\infty$, the top $k$ paths converge to the same limit as in the free boundary case, as conjectured by Caputo, Ioffe and Wachtel.
