Condamin S, Bénichou O, Moreau M
Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), Case Courrier 121, Université Paris 6, 4 Place Jussieu, 75255 Paris Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Feb;75(2 Pt 1):021111. doi: 10.1103/PhysRevE.75.021111. Epub 2007 Feb 13.
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a sphere. In both cases, we also discuss the case of two targets, including splitting probabilities and conditional mean first-passage times. In addition, we study the higher-order moments and the full distribution of the first-passage time. These results significantly extend our earlier contribution [Condamin, Phys. Rev. Lett. 95, 260601 (2005)].
在本文中，我们给出了离散有界晶格中随机游走从起始位点到目标位点的平均首次通过时间的计算结果，以及有界域中布朗运动（目标为球体）的平均首次通过时间的计算结果。在这两种情况下，我们还讨论了两个目标的情况，包括分裂概率和条件平均首次通过时间。此外，我们研究了首次通过时间的高阶矩和完整分布。这些结果显著扩展了我们早期的贡献[康达曼，《物理评论快报》95，260601(2005)]。
