论文标题
受约束的非交叉布朗动作，费米斯和法拉利 - 史波斯分布
Constrained non-crossing Brownian motions, fermions and the Ferrari-Spohn distribution
论文作者
论文摘要
条件随机过程可以显示与无条件过程的截然不同的行为。特别是，即使无条件的过程是高斯，有条件的过程也会表现出非高斯波动。在这项工作中，我们重新审视了布朗桥的法拉利 - 斯波斯模型，该模型条件避免了移动的壁，从而将系统推向了大型传播方案。我们将该模型扩展到非跨布朗尼桥的任意数字$ n $。我们在中间时间以$ n \ times n $矩阵的决定因素的形式获得了布朗颗粒距离的距离的联合分布，该矩阵的条目是根据通风函数给出的。我们表明，这种分布与$ n $无旋转的非互动费米子的位置相吻合，被硬墙的线性电势捕获。然后，我们探索系统的$ n \ gg 1 $行为。为了简单起见，我们关注的是，半圆作为时间的函数给出墙壁的位置，但我们希望我们的结果对任何凹墙功能有效。
A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work, we revisit the Ferrari-Spohn model of a Brownian bridge conditioned to avoid a moving wall, which pushes the system into a large-deviation regime. We extend this model to an arbitrary number $N$ of non-crossing Brownian bridges. We obtain the joint distribution of the distances of the Brownian particles from the wall at an intermediate time in the form of the determinant of an $N\times N$ matrix whose entries are given in terms of the Airy function. We show that this distribution coincides with that of the positions of $N$ spinless noninteracting fermions trapped by a linear potential with a hard wall. We then explore the $N \gg 1$ behavior of the system. For simplicity we focus on the case where the wall's position is given by a semicircle as a function of time, but we expect our results to be valid for any concave wall function.
