Caio Alves (Universität Leipzig, Germany)
Conditional decoupling of random interlacements
We briefly review the definition and motivation for the random interlacements process introduced by A.S Sznitman in his seminal paper "Vacant set of random interlacements and percolation" (Annals of Mathematics, 2010). We then proceed to list the recent results obtained for this model, focusing on the percolative properties of the vacant and occupied set. We mention that one of the main difficulties in working with this process is the slow decay of spatial correlations. Using techniques developed by S. Popov and A. Teixeira in "Soft local times and decoupling of random interlacements" (Journal of the European Mathematical Society, 2015) we present a result that aims to circumvent this difficulty, a conditional decoupling inequality.