Département de mathématiques et applications

Cutoff phenomenon for asymmetric zero range process with monotone rates

We investigate the mixing time of the asymmetric Zero Range process on the segment with a nondecreasing rate. We establish that the cutoff holds in the totally asymmetric case with a convex flux, and also with a concave flux if the asymmetry is strong enough. We show that the mix...

From Morse functions to Lefschetz fibrations on cotangent bundles

We prove that, for any Morse function on a compact manifold and any adapted gradient satisfying the Morse–Smale condition, there is a homotopically unique complex-valued symplectic Lefschetz fibration on the cotangent bundle whose restriction to the zero-section is the given func...

Weak-Strong Uniqueness for the Landau Equation by a Relative Entropy Method

Abstract. We derive a weak-strong uniqueness and stability principle for the Landau equation in the soft potentials case (including Coulomb interactions). The distance between two solutions is measured by their relative entropy, which to our knowledge was never used before in sta...