In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and edge sets but with different (possibly 0) weights in each step. This is a very wide class of RW, which includes some well known types of RW as special cases (e.g. reinforced RW, true SAW). We define and explore various possible properties of such walks, and provide criteria for recurrence and transience when the underlying graph is $\mathbb{N}$ or a tree. We provide an example of such a process on $\mathbb{Z}^2$ where conductances can only change from $1$ to $2$ (once for each edge) but nevertheless the walk is transient, and conjecture that such behaviour cannot happen when the weights are chosen in advance, that is, do not depend on the location of the RW.

中文翻译：

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在不断变化的环境中随机游走

在本文中，我们介绍了在变化环境中的随机游走的概念——一种随机游走，其中每一步都在同一组顶点的不同图中执行，或者更一般地说，在相同的顶点和边集上进行加权随机游走，但在每个步骤中具有不同（可能为 0）的权重。这是一类非常广泛的 RW，其中包括一些众所周知的 RW 类型作为特殊情况（例如增强型 RW、真正的 SAW）。我们定义并探索了此类游走的各种可能属性，并在底层图是 $\mathbb{N}$ 或树时提供了递归和瞬态的标准。我们在 $\mathbb{Z}^2$ 上提供了这样一个过程的例子，其中电导只能从 $1$ 变为 $2$（每条边一次）但是游走是瞬态的，并且推测这种行为不会发生预先选择权重，