Non-equilibrium Dynamics and Random Matrices

We prove a quantitative Brunn-Minkowski inequality for sets \(E\) and \(K\), one of which, \(K\), is assumed convex, but without assumption on the other set. We are primarily interested in the case in which \(K\) is a ball. We use this to prove an estimate on the remainder in the Riesz rearrangement inequality under certain conditions on the three functions involved that are relevant to a problem arising in statistical mechanics: This is joint work with Franceso Maggi.