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Local limits and harmonic functions for nonisotropic random walks on free groups. (English) Zbl 0562.60011

Nearest neighbour random walks on the homogeneous tree representing a free group with s generators \((2\leq s<\infty)\) 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 the r-harmonic function connected with the local limits.

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60G50 Sums of independent random variables; random walks
60F05 Central limit and other weak theorems
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