Appears in collection : 2017 - T3 - WS1 - Operator algebras and quantum information theory

Non-locality is certified by the existence of quantum bipartite correlations which are non-explainable by any classical model. Once we know the existence of these, we are faced with the question of how generic is non-locality among quantum correlations. In this talk I will explain recent results where we show that, under quite general assumptions on the considered distribution, a random correlation which lies on the border of the quantum set is with high probability outside the classical set. Moreover, we provide a Bell inequality certifying this fact. From the mathematical point of view, our results require precise estimates of tensor norms or random matrices.