  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.
