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Rate of escape of random walks on wreath products and related groups. (English) Zbl 1051.60047
The author proves analogues of the law of the iterated logarithm for random walks on wreath products and related groups. For groups of polynomial growth, such results can be found in [W. Hebisch and L. Saloff-Coste, Ann. Probab. 21, No. 2, 673–709 (1993; Zbl 0776.60086)], for those with exponential growth and linear escape rate see A. M. Vershik [Russ. Math. Surv. 55, No. 4, 667–733 (2000); translation from Usp. Mat. Nauk 55, No. 4, 59–128 (2000; Zbl 0991.37005)]. Here, the groups studied have exponential growth but sublinear escape rate. Concrete examples studied include Lamplighter groups, Baumslag-Solitar groups and a discrete version of the Sol geometry.

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