论文标题
跳跃过程的分裂概率
Splitting Probabilities of Jump Processes
论文作者
论文摘要
We derive a universal, exact asymptotic form of the splitting probability for symmetric continuous jump processes, which quantifies the probability $ π_{0,\underline{x}}(x_0)$ that the process crosses $x$ before 0 starting from a given position $x_0\in[0,x]$ in the regime $x_0\ll x$.该分析特别是对传输概率的完全明确确定（$ x_0 = 0 $），与微不足道的预测$π_{0，\ usew usewsionline {x}}（0）= 0 $形成鲜明对比，这表明了该过程的连续限制，从而揭示了微观属性属性的重要性。这些结果通过跳跃过程的范式模型进行了说明，并在现实的3 $ slab几何形状中使用了异质媒体中的光散射。在这种情况下，我们对传输概率的明确预测可以直接通过实验进行测量，它提供了描述介质中光散射的有效随机过程的定量表征。
We derive a universal, exact asymptotic form of the splitting probability for symmetric continuous jump processes, which quantifies the probability $ π_{0,\underline{x}}(x_0)$ that the process crosses $x$ before 0 starting from a given position $x_0\in[0,x]$ in the regime $x_0\ll x$. This analysis provides in particular a fully explicit determination of the transmission probability ($x_0=0$), in striking contrast with the trivial prediction $ π_{0,\underline{x}}(0)=0$ obtained by taking the continuous limit of the process, which reveals the importance of the microscopic properties of the dynamics. These results are illustrated with paradigmatic models of jump processes with applications to light scattering in heterogeneous media in realistic 3$d$ slab geometries. In this context, our explicit predictions of the transmission probability, which can be directly measured experimentally, provide a quantitative characterization of the effective random process describing light scattering in the medium.
