On Fractional Brownian Motion Limits in One Dimensional Nearest-neighbor Symmetric Simple Exclusion

Abstract. A well-known result with respect to the one dimensional nearestneighbor symmetric simple exclusion process is the convergence to fractional Brownian motion with Hurst parameter 1/4, in the sense of finite-dimensional distributions, of the subdiffusively rescaled current across the origin, and the subdiffusively rescaled tagged particle position. The purpose of this note is to improve this convergence to a functional central limit theorem, with respect to the uniform topology, and so complete the solution to a conjecture in the literature with respect to simple exclusion processes.