Let G be a finite group and E a generating set for G. Let P be a probability measure on G whose support is E. We define a random walk on G as follows. At the zeroth stage, we set w 0 =1. At the k th stage, we set w k =w k&1 x, where x # E is chosen with probability P(x). For g # G, the probability t
Random walks on groups
✍ Scribed by Lajos Takács
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 874 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The Green function of an arbitrary, finitely supported random walk on a discrete group with context-free word problem is algebraic. It is shown how this theorem can be deduced from basic results of formal language theory. Context-free groups are precisely the finite extensions of free groups.
The classical gambler's ruin problem, i.e., a random walk along a line may be viewed q raph theoretically as a random walk along a path with the endpoints as absorbing states. This paper is an i0vestigation of the natural generalization of this problem to that of a particle walking randomly on a tre
Random walks (RWs) and related stochastic techniques have become ubiquitous tools in many areas of physics recently. Fractals are no exception. Random walks on fractals have an added interest: random walk trails (e.g. sample paths of Brownian motion) are themselves fractal in general, and interestin