Seminar at SMU Delhi

This talk is an attempt to introduce, with as little technicalities as possible, the basic elements of non-commutative probability. This will be done by drawing parallels with classical moments and cumulants of random variables with their analogues in the non-commutative world. The idea of free independence, which is the analogue of classical independence will be introduced. If time permits, we shall show applications in random matrices and in statistical analysis in high dimensional models.