The Poisson boundary of random rational affinities

Details The Poisson boundary of random rational affinities The Poisson boundary of random rational affinities

2004-03-11

arxiv.org/abs/math/0403198v1

Mathematics

Probability

13 pages

Scientific paper

The group of affine transformations with rational coefficients acts naturally
on the real line, but also on the $p$-adic fields. The aim of this note is to
show that, for random walks whose laws have a finite first moment, all these
actions are necessary and sufficient to describe the Poisson boundary, which is
in fact the product of all the fields that contract in mean.

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