Invariant random subgroups of strictly diagonal limits of finite symmetric groups

We classify the ergodic invariant random subgroups of strictly diagonal limits of finite symmetric groups

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