Europe/Lisbon
Room P3.10, Mathematics Building Instituto Superior Técnicohttps://tecnico.ulisboa.pt

Tertuliano Franco
, Universidade Federal da Bahia

In this work, we deal with the symmetric exclusion process with k slow bonds equally spaced in the torus with kn sites, where the strength of a slow bond is $\alpha n^{-\beta}$, where $\beta>1$. For k fixed, it was known (T. Franco, P. Gonçalves, A. Neumann, AIHP'13) that the hydrodynamic limit in the diffusive scaling of this process is given by the heat equation with Neumann boundary conditions, meaning that the system does not allow flux through a slow bond in the limit. In this joint work with Tiecheng Xu and Dirk Erhard, we obtain another three superdiffusive scalings for this system. If $k$ is fixed and the (time) scaling is $n^{\theta}$, where $2< \theta<1+\beta$, the system reaches equilibrium instantaneously at each box between two consecutive slow bonds, being constant in time and space. If k is fixed and $\theta=1+\beta$, the density is spatially constant inside each box, and evolves as the discrete heat equation. And if $\theta=1+\beta$ and $k$ goes to infinity, we recover the continuous heat equation (on the torus).