Poisson boundary for finitely generated groups of rational affinities
The group of affine transformations with rational coefficients, $aff(Q)$, acts naturally on the real line, but also on the $p$-adic fields. The aim of this note is to show that all these actions are necessary and sufficient to represent bounded $\mu$-harmonic functions for a probability measure $\mu...
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| Main Author: | |
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| Format: | Journal Article |
| Language: | English |
| Published: |
11-03-2004
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | The group of affine transformations with rational coefficients, $aff(Q)$,
acts naturally on the real line, but also on the $p$-adic fields. The aim of
this note is to show that all these actions are necessary and sufficient to
represent bounded $\mu$-harmonic functions for a probability measure $\mu$ on
$aff(Q)$ that is supported by a finitely generated sub-group, that is to
describe the Poisson boundary. |
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| DOI: | 10.48550/arxiv.math/0403197 |