Transience of algebraic varieties in linear groups and application to generic Zariski density

Details Transience of algebraic varieties in linear groups and application to generic Zariski density Transience of algebraic varieties in linear groups and application to generic Zariski density

2011-03-04

arxiv.org/abs/1103.0944v1

Mathematics

Group Theory

Scientific paper

We study the transience of algebraic varieties in linear groups. In particular, we show that a "non elementary" random walk in SL_2(R) escapes exponentially fast from every proper algebraic subvariety. We also treat the case where the random walk is on the real points of a semi-simple split algebraic group and show such a result for a wide family of random walks. As an application, we prove that generic subgroups (in some sense) of linear groups are Zariski dense.

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