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Titlebook: Random Walks on Reductive Groups; Yves Benoist,Jean-François Quint Book 2016 Springer International Publishing AG 2016 Markov chain.Martin

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Loxodromic ElementsWe prove the existence of loxodromic elements in Zariski dense subgroups of semisimple real Lie groups.
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The Jordan Projection of SemigroupsFor Zariski dense subgroups of semisimple real Lie groups, we prove the convexity and non-degeneracy of the limit cone. We also prove the density of the group spanned by the Jordan projections.
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Transfer Operators over Contracting ActionsWe focus on cocycles over a contracting action. We study the spectral properties of the corresponding complex transfer operators for small values of the parameter.
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Limit Laws for CocyclesWe prove the Central Limit Theorem, the Law of Iterated Logarithm and the Large Deviation Principle for a cocycle over a contracting action.
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