Article contents
Random walks on a dodecahedron
Published online by Cambridge University Press: 14 July 2016
Abstract
We consider the general Markov chain on the vertices of a regular dodecahedron D such that P[Xn+1 = j | Xn = i] depends only on the distance between i and j. We consider also a Markov chain on the oriented edges (i, j) of D for which the only non-zero transition probabilities are and fix a vertex A. This paper computes explicitly P[Xn = A | X0 = A] and P[In = A | I0 = A]. The methods used are applicable to other solids.
Keywords
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 1980
Footnotes
The paper was prepared while this author was in residence at Case Western Reserve University as Visiting Professor of Mathematics and Statistics.
References
- 10
- Cited by