Poisson boundary of $GL_d(\Q)$

Sara Brofferio; Bruno Schapira

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arXiv · 0906.5548

Poisson boundary of $GL_d(\Q)$

Sara Brofferio·Bruno Schapira

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Abstract

We construct the Poisson boundary for a random walk supported by the general linear group on the rational numbers as the product of flag manifolds over the $p$-adic fields. To this purpose, we prove a law of large numbers using the Oseledets' multiplicative ergodic theorem.

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Sara Brofferio, Bruno Schapira. 2009-11-17. Poisson boundary of $GL_d(\Q)$. https://arxiv.org/abs/0906.5548

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