Matinée scientifique en physique mathématique

--10h Sabine Jansen (Munich), Intensity of a Gibbs point process and an abstract inversion theorem

The intensity of a Gibbs point process (density) is a highly non-trivial function of the intensity of the underlying Poisson point process (activity). In statistical physics it is often of interest to  compute not only this relation but also its inverse relation. The talk presents an abstract inversion theorem on mappings between spaces of measures and explains how it applies to the intensity of a Gibbs point process when the overall intensity is small. The inversion theorem applies even when the conditions of a Banach inversion theorem are not met and allows one to bypass more complicated setups such as Nash-Moser; instead a crucial role is played by trees and their recursive structure. Based on joint work with Tobias Kuna and Dimitrios Tsagkarogiannis (J, Funct. Anal. 2023).



--11h Thomas Leblé (Paris), Gradient flow of the infinite-volume free energy for short-range lattice systems with continuous spins

We consider an infinite lattice system of spins living on a smooth compact manifold, with short-range interactions, and we construct the gradient flow for its infinite-volume free energy using an adaptation of the variational approach in Wasserstein space pioneered by Jordan-Kinderlehrer-Otto.

We prove that the trajectories of the gradient flow and those of the law of the spins under the associated overdamped Langevin dynamics satisfy the same infinite-volume Fokker-Planck-Kolmogorov equation. We prove regularity of weak solutions and derive an Evolution Variational Inequality for regular solutions, which implies uniqueness, and thus that trajectories of the gradient flow coincide with those obtained from the Langevin dynamics. Based on joint work with Ronan Herry.