Reinforced Random Walks and Adic Transformations
Reinforced Random Walks and Adic Transformations
复制标题
强化随机游走和 Adic 变换
DOI：
10.1007/s10959-010-0282-y
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发表时间：
2010
影响因子：
0.8
通讯作者：
K. Petersen
中科院分区：
文献类型：
--
作者：
S. Frick;K. Petersen
对于一个给定的有限图，我们关联三种进，或Bratteli-Vershik，系统：固定，符号计数，和加强。我们给出了自然行走测度是渐近不变的条件，并确定了遍历的渐近不变测度的一些类的例子。如果步行测度是adic-invariant，我们将其遍历分解与极限边遍历频率向量联系起来。对于某些特殊的非简单强化方案，我们明确地计算了边遍历频率的密度函数。
To a given finite graph we associate three kinds of adic, or Bratteli–Vershik, systems: stationary, symbol-count, and reinforced. We give conditions for the natural walk measure to be adic-invariant and identify the ergodic adic-invariant measures for some classes of examples. If the walk measure is adic-invariant, we relate its ergodic decomposition to the vector of limiting edge traversal frequencies. For some particular nonsimple reinforcement schemes, we calculate the density function of the edge traversal frequencies explicitly.