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Nearest neighbour random walks on free products of discrete groups. (English) Zbl 0627.60012
The author’s main result is a relation between the Green functions of random walks on groups \(G_ i\) and the Green function of an induced random walk on the free product of these groups \(G_ i\). This relation is derived by using combinatorial and probabilistic methods. As consequences the author gets a formula for the norm of associated convolution operators and a general local limit theorem of the type \[ p^{(n)}(x,y)\sim C(x,y)r^ nn^{-3/2}\quad (for\quad n\to \infty), \] were C(x,y) and r are determined. The paper is elegant and well written. Very similar results where also obtained by D. I. Cartwright and P. M. Soardi [Nagoya Math. J. 102, 163-180 (1986; Zbl 0581.60055)] using a functional analytic method.
Reviewer: P.Gerl

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60G50 Sums of independent random variables; random walks