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Random walks on amalgams. (English) Zbl 0564.60069
Let \(\Gamma\) be a locally compact amalgam of compact groups. The action of \(\Gamma\) on a suitable tree is used to study all random walks on \(\Gamma\) which can be described as nearest neighbour random walks on the tree. In particular, local limit theorems are derived, i.e. the asymptotic behaviour of n-step transition probabilities is determined.

MSC:
60G50 Sums of independent random variables; random walks
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
43A05 Measures on groups and semigroups, etc.
05C05 Trees
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