# abstract

Analysis Seminar | |

Topic: | An application of displacement convexity at the level of point processes |

Speaker: | Thomas Leblé |

Affiliation: | Member, School of Mathematics |

Date: | Monday, November 11 |

Time/Room: | 5:00pm - 6:00pm/Simonyi Hall 101 |

Video Link: | https://video.ias.edu/analysis/2019/1111-ThomasLeblé |

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.