Analysis Seminar

The path between two measures in the sense of optimal transport yields the notion of *displacement interpolation*. As observed by R. McCann, certain functionals that are not convex in the usual sense are nonetheless *displacement convex*. Following an idea of A. Guionnet, we define a notion of displacement convexity at the level of point processes seen as measures on \R^{\Z}, and use it to prove that a certain free energy functional, arising in Hermitian random matrix theory has a unique minimiser. This tells us something about certain systems of particles in 1d. Joint work with M. Erbar and M. Huesmann.