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On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion. (English) Zbl 1162.60347
Summary: A well-known result with respect to the one dimensional nearest-neighbor 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.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
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