Phase transition in equilibrium fluctuations of symmetric slowed exclusion

Abstract

We analyze the equilibrium fluctuations of the density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow bond where it is $\alpha n^-\beta$, where $\alpha,\beta\geq{0}$ and $n$ is the scaling parameter. Depending on the regime of $\beta$, we find three different behaviors for the limiting fluctuations whose covariances are explicitly computed. In particular, for the critical value $\beta=1$, starting a tagged particle near the slow bond, we obtain a family of gaussian processes indexed in $\alpha$, interpolating a fractional brownian motion of Hurst exponent 1/4 and the degenerate process equal to zero.