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 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 ≫ 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.

条件随机过程可以显示与无条件过程非常不同的行为。特别是，即使无条件过程是高斯过程，条件过程也可能表现出非高斯波动。在这项工作中，我们重新审视了布朗桥的 Ferrari-Spohn 模型，该模型有条件避免移动墙，这将系统推入大偏差状态。我们将此模型扩展到任意数量N的非交叉布朗桥。我们以N N矩阵的行列式的形式获得布朗粒子在中间时间与壁的距离的联合分布，该矩阵的条目根据艾里函数给出。我们表明这种分布与N的位置的分布一致由具有硬壁的线性势所困的无自旋非相互作用费米子。然后我们探索系统的N ≫ 1 行为。为简单起见，我们关注墙的位置由半圆给出作为时间的函数的情况，但我们希望我们的结果对任何凹墙函数都有效。