二维随机取向曼哈顿格是暂态的
The randomly oriented Manhattan lattice in 2D is transient
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中文总结 AI 辅助
本文证明二维随机取向曼哈顿格上的行走几乎必然暂态，采用简短变分论证，验证Redner的均方位移预测。
中文摘要 AI 辅助
独立地以公平硬币为$\mathbb{Z}^2$的每条水平线和垂直线定向。一个行走者以等概率选择通过其当前位置的两条线之一，并沿该线的方向走一步。Redner（1989）引入此行走作为各向同性随机速度场中输运的模型，并预测其均方位移按$n^{2/3}$增长。我们证明该行走几乎必然暂态。证明是一个简短的变分论证。
英文摘要
Independently orient each horizontal and vertical line of $\mathbb{Z}^2$ by a fair coin. A walker chooses one of the two lines through its current position with equal probability and takes one step in the direction of that line. Redner (1989) introduced this walk as a model of transport in an isotropic random velocity field and predicted that its root-mean-square displacement grows like $n^{2/3}$. We prove that the walk is transient almost surely. The proof is a short variational argument.
