Quenched nonequilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder

For a sequence of i.i.d. random variables $\{{\xi }_x:x\in \text{bb}Z\}$ bounded above and below by strictly positive finite constants, consider the nearest-neighbor one-dimensional simple exclusion process in which a particle at $x$ (resp. $x+1$) jumps to $x+1$ (resp. $x$) at rate ${\xi }_x$. We examine a quenched nonequilibrium central limit theorem for the position of a tagged particle in the exclusion process with bond disorder $\{{\xi }_x:x\in \text{bb}Z\}$. We prove that the position of the tagged particle converges under diffusive scaling to a Gaussian process if the other particles are initially distributed according to a Bernoulli product measure associated to a smooth profile ${\rho }_0:\text{bb}R\to [0,1]$.