占领时间在一个梳子与分叉的牙齿
Occupation times on a comb with ramified teeth
摘要：
本文研究了梳齿上随机游动的占用时间统计。这是通过占用时间和第一次通过时间之间的关系来实现的。半空间中的占据时间的统计服从兰珀提分布，即广义反正弦定律成立。观察到不同行为之间的过渡，这是由梳的骨干和齿的大小，以及偏见控制。利用平均场论和数值模拟分析了非单连通区域上的占据时间。在这种情况下，广义反正弦定律是无效的。
英文摘要：
We investigate occupation time statistics for random walks on a comb with ramified teeth. This is achieved through the relation between the occupation time and the first passage times. Statistics of occupation times in half space follows Lamperti's distribution, i.e. the generalized arcsine law holds. Transitions between different behaviors are observed, which are controlled by the size of the backbone and teeth of the comb, as well as bias. Occupation time on a non-simply connected domain is analyzed with a mean-field theory and numerical simulations. In that case, the generalized arcsine law isn't valid.
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