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1 results

Random walks on a dodecahedron
G. Letac, L. Takács
Journal:

Journal of Applied Probability / Volume 17 / Issue 2 / June 1980

Published online by Cambridge University Press:

14 July 2016, pp. 373-384

Print publication:

June 1980
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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.