  For Sina\"i's walk (X_k) we show that the empirical measure of the
environment seen from the particle (\bar\w_k) converges in law to some random
measure S. This limit measure is explicitly given in terms of the infinite
valley, which construction goes back to Golosov. As a consequence an "in law"
ergodic theorem holds for additive functionals of (\bar\w_k) . When the limit
in this "in law" ergodic theorem is deterministic, it holds in probability.
This allows some extensions to the recurrent case of the ballistic
"environment's method" dating back to Kozlov and Molchanov. In particular, we
show an LLN and a mixed CLT for the sums sum_{k=1}^nf(\Delta X_k), where f is
bounded and depending on the steps \Delta X_k:=X_{k+1}-X_k.
