| Abstract: | We consider the weakly asymmetric simple exclusion process in the presence of a slow bond and starting from the invariant state, namely the Bernoulli product measure of parameter ({rho in (0,1)}). The rate of passage of particles to the right (resp. left) is ({frac{1}{2} + frac{a}{2n^{gamma}}}) (resp. ({frac{1}{2} - frac{a}{2n^{gamma}}})) except at the bond of vertices ({{-1,0}}) where the rate to the right (resp. left) is given by ({frac{alpha}{2n^beta} + frac{a}{2n^{gamma}}}) (resp. ({frac{alpha}{2n^beta}-frac{a}{2n^{gamma}}})). Above, ({alpha > 0}), ({gamma geq beta geq 0}), ({ageq 0}). For ({beta < 1}), we show that the limit density fluctuation field is an Ornstein–Uhlenbeck process defined on the Schwartz space if ({gamma > frac{1}{2}}), while for ({gamma = frac{1}{2}}) it is an energy solution of the stochastic Burgers equation. For ({gamma geq beta =1}), it is an Ornstein–Uhlenbeck process associated to the heat equation with Robin’s boundary conditions. For ({gamma geq beta > 1}), the limit density fluctuation field is an Ornstein–Uhlenbeck process associated to the heat equation with Neumann’s boundary conditions. |
