Seminário de Análise, Geometria e Sistemas Dinâmicos

Asymptotic behavior of the exclusion process with slow boundary

The system of interacting particles that will be presented (the exclusion process with slow boundary) arouses considerable interest in its applicability, for modeling mass transfer between reservoirs with different densities. But it also arouses interest in its theoretical part because of its non-triviality, for example: the invariant measure is given through matrices of Ansatz, see Derrida. Another interesting theoretical aspect, which will be the main focus of this talk, is the behavior of particles density (hydrodynamic limit) is given by the heat equation with boundary conditions. These boundary conditions have phase transition, which depends on how slow the behavior at the border is. More specifically, if the boundary has transfer rate of the order of $N^{- a}$, where $N$ is the scale parameter and $a$ is a fixed non-negative real number, then we get for $a$ in $[0,1)$, Dirichlet boundary conditions, for $a\gt 1$ Neumann boundary conditions and the critical case is when $a=1$, which has Robin boundary conditions. In this talk, in addition to the hydrodynamic limit, other results for the scale limits of this model will be presented, such as fluctuations and large deviations.