Abstract
Let G be a locally compact group, E a homogeneous space of G. We discuss the relations between recurrence of a random walk on G or E, ergodicity of the corresponding transformations and polynomial growth of G or E. We consider the special case of linear groups over local fields.
Mathematics Subject Classification (2000). 22E30, 31C12, 37A17, 37A50.
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Guivarc’h, Y., Raja, C.R.E. (2011). Polynomial Growth, Recurrence and Ergodicity for Random Walks on Locally Compact Groups and Homogeneous Spaces. In: Lenz, D., Sobieczky, F., Woess, W. (eds) Random Walks, Boundaries and Spectra. Progress in Probability, vol 64. Springer, Basel. https://doi.org/10.1007/978-3-0346-0244-0_4
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DOI: https://doi.org/10.1007/978-3-0346-0244-0_4
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