Diaconis, Persi; Saloff-Coste, Laurent An application of Harnack inequalities to random walk on nilpotent quotients. (English) Zbl 0889.60008 J. Fourier Anal. Appl. Spec. Iss., 189-207 (1995). 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. Cited in 14 Documents MSC: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization 43A05 Measures on groups and semigroups, etc. Keywords:random walks; spaces of nilpotent groups; Cayley graph; Harnack inequality Citations:Zbl 0776.60086 PDFBibTeX XMLCite \textit{P. Diaconis} and \textit{L. Saloff-Coste}, J. Fourier Anal. Appl., 189--207 (1995; Zbl 0889.60008)