Poisson boundary of $GL_d(\Q)$

Details Poisson boundary of $GL_d(\Q)$ Poisson boundary of $GL_d(\Q)$

2009-06-30

arxiv.org/abs/0906.5548v2

Mathematics

Probability

minor corrections, more details in the introduction

Scientific paper

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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