  We introduce the voter model on the infinite lattice with a slow membrane and
investigate its hydrodynamic behavior and nonequilibrium fluctuations. The
model is defined as follows: a voter adopts one of its neighbors' opinion at
rate one except for neighbors crossing the hyperplane $\{x:x_1 = 1/2\}$, where
the rate is $\alpha N^{-\beta}$. Above, $\alpha>0,\,\beta \geq 0$ are two
parameters and $N$ is the scaling parameter. The hydrodynamic equation turns
out to be heat equation with various boundary conditions depending on the value
of $\beta$. For the nonequilibrium fluctuations, the limit is described by
generalized Ornstein-Uhlenbeck process with certain boundary condition
corresponding to the hydrodynamic equation.
