论文标题
Z^2上的简单随机步行在轴上扰动（更新情况）
Simple random walk on Z^2 perturbed on the axis (renewal case)
论文作者
论文摘要
我们在Z^2上研究一个简单的随机步行，并在轴上有限制。当颗粒（例如，参见[DAL88]）提交到局部场时，动机来自物理学。在我们的情况下，我们假设粒子在锥体中自由演变，但是在接触轴时，力将其逐渐向原点推回。主要结果证明，该力可以以一种更新结构出现在随机行走的轨迹中出现的方式。这意味着仅限于轴的轨迹部分存在千古的结果。
We study a simple random walk on Z^2 with constraints on the axis. Motivation comes from physics when particles (a gas for example, see [Dal88]) are submitted to a local field. In our case we assume that the particle evolves freely in the cones but when touching the axis a force pushes it back progressively to the origin. The main result proves that this force can be parametrized in such a way that a renewal structure appears in the trajectory of the random walk. This implies the existence of an ergodic result for the parts of the trajectory restricted to the axis.
