循环群和亚阿贝尔群上随机游动的逃逸率
The rate of escape of random walks on polycyclic and metabelian groups
摘要：
利用子群畸变来确定一类多环群上简单随机游动的逃逸率，并证明了逃逸率在生成集变化时不变.对于亚阿贝尔群，我们定义了一种更强的子群畸变形式，它适用于非非线性生成的子群。在此假设下，我们计算的逃逸率为某些随机游动的亚阿贝尔群通过比较的耗散阿贝尔沙堆倾倒。
英文摘要：
We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion, which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on metabelian groups via a comparison to the toppling of a dissipative abelian sandpile.
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