Abstract
We apply the previous results to random walks in products of algebraic reductive groups over local fields. We prove a Local Limit Theorem with target and with moderate deviations for the Iwasawa cocycle and for the Cartan projection. For the random walks on the linear groups, we deduce a Local Limit Theorem for the norms of matrices and for the norms of vectors.
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© 2016 Springer International Publishing AG
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Benoist, Y., Quint, JF. (2016). The Local Limit Theorem for Products of Random Matrices. In: Random Walks on Reductive Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 62. Springer, Cham. https://doi.org/10.1007/978-3-319-47721-3_17
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DOI: https://doi.org/10.1007/978-3-319-47721-3_17
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47719-0
Online ISBN: 978-3-319-47721-3
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