Biased Random Walk Conditioned on Survival Among Bernoulli Obstacles: Subcritical Phase
Biased Random Walk Conditioned on Survival Among Bernoulli Obstacles: Subcritical Phase
复制标题
以伯努利障碍中的生存为条件的有偏随机游走：亚临界阶段
DOI：
10.1007/s00220-019-03644-9
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发表时间：
2020
影响因子：
2.4
通讯作者：
Xu Changji
中科院分区：
文献类型：
--
作者：
Ding Jian;Fukushima Ryoki;Sun Rongfeng;Xu Changji
我们考虑离散时间有偏随机游动条件，以避免伯努利障碍（）到timeN。已知该模型经历相变：对于大的偏置，行走是弹道的，而对于小的偏置，它是亚弹道的。我们证明，在子弹道阶段，随机游动包含在一个球的半径，这是相同的规模为无偏的情况下。作为一个中间步骤，我们还证明了大偏差原则的端点分布的无偏随机游走在尺度之间。这些结果改进并补充了Sznitman的早期工作（Ann Sci École Norm Sup（4），28（3）：345-370，371-390，1995）。
We consider a discrete time biased random walk conditioned to avoid Bernoulli obstacles on() up to timeN. This model is known to undergo a phase transition: for a large bias, the walk is ballistic whereas for a small bias, it is sub-ballistic. We prove that in the sub-ballistic phase, the random walk is contained in a ball of radius, which is the same scale as for the unbiased case. As an intermediate step, we also prove large deviation principles for the endpoint distribution for the unbiased random walk at scales betweenand. These results improve and complement earlier work by Sznitman (Ann Sci École Norm Sup (4), 28(3):345–370, 371–390, 1995).