Hierarchical pinning model with site disorder: Disorder is marginally relevant

We study a hierarchical disordered pinning model with site disorder for which, like in the bond disordered case [6, 9], there exists a value of a parameter b (enters in the definition of the hierarchical lattice) that separates an irrelevant disorder regime and a relevant disorder regime. We show that for such a value of b the critical point of the disordered system is different from the critical point of the annealed version of the model. The proof goes beyond the technique used in [9] and it takes explicitly advantage of the inhomogeneous character of the Green function of the model.Comment: 13 pages, 1 figure, final version accepted for publication. to appear in Probability Theory and Related Field

The Origin of early Li-6 and the Reionization of the Universe

Observational data on the early galactic abundances of the light elements lithium, beryllium and boron are combined with data related to the reionization of the intergalactic medium (IGM) in a search of processes happening in the early universe. Early massive metal-free stars (Pop III), largely held responsible for the reionization of the IGM, are proposed to have been also at the origin of the lithium-6 plateau, through their winds. In this sense the evolution of the Li-6/Be-9 ratio appears to be a key parameter for the history of nucleosynthesis, as a monitor of the early formation of metals and their subsequent injection in high energy particles.Comment: 5 pages, no figures, to appear in "Element Stratification in Stars, 40 years of Atomic Diffusion", Eds. G, Alecian, O. Richard and S. Vauclai

The scaling limit of polymer pinning dynamics and a one dimensional Stefan freezing problem

We consider the stochastic evolution of a 1+1-dimensional interface (or polymer) in presence of a substrate. This stochastic process is a dynamical version of the homogeneous pinning model. We start from a configuration far from equilibrium: a polymer with a non-trivial macroscopic height profile, and look at the evolution of a space-time rescaled interface. In two cases, we prove that this rescaled interface has a scaling limit on the diffusive scale (space rescaled by $L$ in both dimensions and time rescaled by $L^2$ where $L$ denotes the length of the interface) which we describe: when the interaction with the substrate is such that the system is unpinned at equilibrium, then the scaling limit of the height profile is given by the solution of the heat equation with Dirichlet boundary condition ; when the attraction to the substrate is infinite, the scaling limit is given a free-boundary problem which belongs to the class of Stefan problems with contracting boundary, also referred to as Stefan freezing problems. In addition, we prove the existence and regularity of the solution to this problem until a maximal time, where the boundaries collide.Comment: 42 pages, 4 figures. The paper contains more results than the first version and the title has been change