The Poisson boundary of random rational affinities

英文摘要：

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.