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An application of Harnack inequalities to random walk on nilpotent quotients. (English) Zbl 0889.60008

Summary: This paper shows that random walks on finite homogeneous spaces of nilpotent groups “get random” in order \(\gamma^2\) steps where \(\gamma\) is the diameter of the associated Cayley graph. The argument uses a Harnack inequality of W. Hebisch and L. Saloff-Coste [Ann. Probab. 21, No. 2, 673-709 (1993; Zbl 0776.60086)]. In contrast, random walks on finite homogeneous spaces of groups satisfying Kazhdan’s property T get random in order \(\gamma\) steps.

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
43A05 Measures on groups and semigroups, etc.

Citations:

Zbl 0776.60086
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