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Abstract: We discuss recurrence and ergodicity properties of random walks andassociated skew products for large classes of locally compact groups andhomogeneous spaces. In particular we show that a closed subgroup of a productof finitely many linear groups over local fields supports a recurrent randomwalk if and only if it has at most quadratic growth. We give also a detailedanalysis of ergodicity properties for special classes of random walks onhomogeneous spaces. The structure of closed subgroups of linear groups overlocal fields and the properties of group actions with respect to stationarymeasures play an important role in the proofs.



Author: Y. Guivarc'h, C. R. E. Raja

Source: https://arxiv.org/



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