Summary
Nearest neighbour random walks on the homogeneous tree representing a free group withs generators (2≦s∞) are investigated. By use of generating functions and their analytic properties a local limit theorem is derived. A study of the harmonic functions corresponding to the random walk leads to properties that characterize ther-harmonic function connected with the local limits.
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Gerl, P., Woess, W. Local limits and harmonic functions for nonisotropic random walks on free groups. Probab. Th. Rel. Fields 71, 341–355 (1986). https://doi.org/10.1007/BF01000210
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DOI: https://doi.org/10.1007/BF01000210