从硬壁附近动力学的精确解到非马尔可夫过程的极值统计
From an exact solution of dynamics in the vicinity of hard walls to extreme value statistics of non-Markovian processes
AI总结：
本研究提出硬壁附近一维过阻尼动力学精确解，建立受限稳态分布与无约束随机过程极值统计的映射，将其应用于布朗运动并拓展至非马尔可夫过程，计算了两类粒子的长时间不交叉概率。
摘要：
我们提出了硬壁附近一维过阻尼动力学的精确解，借此可将受限条件下的稳态分布与无约束随机过程的极值统计关联起来。这一映射关系不受驱动动力学的噪声统计特性的影响。我们首先将该结果应用于布朗运动理论，推导了布朗路径与一类特定曲线的不交叉概率，由此可统一推导出该领域的若干已知结果。随后我们将分析拓展至非马尔可夫过程，利用到稳态的映射，计算了一对run-and-tumble（奔跑-翻滚）粒子与布朗粒子的长时间不交叉概率。
英文摘要：
We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping holds regardless of the statistics of the noise driving the dynamics. We first apply this result within Brownian motion theory, deriving the noncrossing probability of a Brownian path with a specific family of curves, from which several well-known results in the field can be recovered in a unified way. We then extend the analysis to non-Markovian processes, using the mapping to a steady-state to compute the long-time noncrossing probability of a pair of run-and-tumble and Brownian particles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
