Summary
Let G be the group generated by L free involutions, whose Cayley graph T is the infinite homogeneous tree with L edges at every node. A general central limit theorem and law of the iterated logarithm is proven for left-invariant random walks Z n on G or T which applies to the distance of Z n from a fixed point, as well as to the distribution of the last R letters in Z n . For nearest neighbor random walks, we also derive a generating function identity that yields formulas for the asymptotic mean and variance of the distance from a fixed point. A generalization for Z n with a finitely supported step distribution is derived and discussed.
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Partially supported by grant NSF MCS85-04315
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Sawyer, S., Steger, T. The rate of escape for anisotropic random walks in a tree. Probab. Th. Rel. Fields 76, 207–230 (1987). https://doi.org/10.1007/BF00319984
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DOI: https://doi.org/10.1007/BF00319984
Keywords
- Generate Function
- Stochastic Process
- Probability Theory
- Limit Theorem
- Statistical Theory