发表机构
Laboratoire de Physique de la Matière Condensée, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris（凝聚态物质物理实验室，法国国家科学研究中心-巴黎综合理工学院，巴黎理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析了部分反应边界平面楔形中布朗粒子生存概率的幂律衰减，通过匹配渐近法确定了持续指数与前置因子，推导了边界局部时间和首通时间的概率密度函数的长时间行为。
AI 中文摘要
我们研究在无限平面楔形区域中扩散的布朗粒子的生存概率的幂律衰减，该楔形的两个侧面为部分反应边界，由Robin边界条件描述。我们采用匹配渐近分析，将长时间渐近行为与顶点附近的稳态调和Robin问题关联起来，该方法可确定任意开口角的持续指数，并对α=π/n（n=1,2,…）的楔形族显式给出前置因子。我们推测顶点前置因子可简单扩展到任意角度，并通过数值验证支持该推测，此渐近行为描述了向完全吸收楔形的已知结果的过渡。作为直接应用，我们还推导了楔形侧面上边界局部时间的概率密度函数，以及相关首通时间的概率密度函数的长时间行为。
英文摘要
We investigate the power-law decay of the survival probability of a Brownian particle diffusing in an infinite planar wedge whose two sides are partially reactive and described by Robin boundary conditions. We employ matched asymptotic analysis to relate the long-time asymptotics to a stationary harmonic Robin problem near the apex. This approach determines the persistence exponent for arbitrary opening angles and yields the prefactor explicitly for the family of wedges with $α=π/n$ ($n=1,2,\ldots$). A simple extension of the apex prefactor to arbitrary angles is conjectured and supported numerically. This asymptotic behavior describes the crossover to the well-known result for perfectly absorbing wedges. As immediate applications, we also deduce the long-time behavior of the probability density function of the boundary local time on wedge sides, as well as the probability density function of the associated first-crossing time.
