Approximations of standard equivalence relations and Bernoulli percolation at p\_u

The goal of this note is to announce certain results in orbit equivalence theory, especially concerning the approximation of p.m.p. standard equivalence relations by increasing sequence of sub-relations, with applications to the behavior of the Bernoulli percolation on graphs at the threshold pu. R'esum'e en Fran\c{c}ais. Approximations de relations d’'equivalence standards et percolation de Bernoulli `a p_u.