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• W1589289969 abstract "We introduce a novel notion of {it local spectral gap} for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action $Gammacurvearrowright G$, whenever $Gamma$ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group $G$. This extends to the non-compact setting recent works of Bourgain and Gamburd cite{BG06,BG10}, and Benoist and de Saxce cite{BdS14}. We present several applications to the Banach-Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on $G$. In particular, we prove that, up to a multiplicative constant, the Haar measure is the unique $Gamma$-invariant finitely additive measure defined on all bounded measurable subsets of $G$." @default.
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• W1589289969 date "2015-03-22" @default.
• W1589289969 modified "2023-09-25" @default.
• W1589289969 title "Local spectral gap in simple Lie groups and applications" @default.
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