论文标题
马尔可夫在小组上随机步行的线性化
Markovian linearization of random walks on groups
论文作者
论文摘要
在运算符代数中，线性化技巧是一种技术，可降低对代数A元素评估的非交通性多项式的研究，以研究对一位学位的多项式研究，并在扩大的代数A X M R（C）上进行了评估。我们介绍了线性化技巧的新实例，该实例是针对G组进行有限支持的随机步行而定制的，而是研究最近的邻居颜色的随机步行，在G x {1，。 ..，r}，这要简单得多。作为应用程序，我们将最接近的邻居步行的众所周知的结果扩展到有限的随机步行中，从而展示了如何获得有限支撑的随机步行的漂移和熵的明确公式。
In operator algebra, the linearization trick is a technique that reduces the study of a non-commutative polynomial evaluated at elements of an algebra A to the study of a polynomial of degree one, evaluated on the enlarged algebra A x M r (C), for some integer r. We introduce a new instance of the linearization trick which is tailored to study a finitely supported random walk on a group G by studying instead a nearest-neighbor colored random walk on G x {1,. .. , r}, which is much simpler to analyze. As an application we extend well-known results for nearest-neighbor walks on free groups and free products of finite groups to colored random walks, thus showing how one can obtain explicit formulas for the drift and entropy of a finitely supported random walk.
