论文标题
从粒子观看的环境和低维度的弹道RWRE放缓
Environment viewed from the particle and slowdown for ballistic RWRE in low dimensions
论文作者
论文摘要
我们考虑在$ \ mathbb {z}^d $下在随机环境中随机步行，在弹道条件下$（t）$。我们显示了从粒子观察到的环境的不变性度量$ q $的存在，以$ d = 2 $和$ d = 3 $，这反驳了关于二维案例中arxiv中的猜想：1405.6819。我们还证明了radon-nikodym衍生品$ dq/dp $的尾巴估计，其中$ p $是环境上的原始分布。最后，我们为$ d = 3 $的再生时间提供几乎尖锐的尾巴界限。
We consider a random walk in a random environment on $\mathbb{Z}^d$ under ballisticity condition $(T)$. We show the existence of the invariant measure $Q$ with respect to the environment viewed from the particle for $d=2$ and $d=3$, which disproves a conjecture made in arXiv:1405.6819 regarding the two-dimensional case. We also prove tail estimates for the Radon-Nikodym derivative $dQ/dP$, where $P$ is the original distribution on the environment. Lastly, we provide nearly sharp tail bounds for regeneration times for $d=3$.
