On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion

Details On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion

2007-10-31

arxiv.org/abs/0711.0017v1

Mathematics

Probability

11 pages

Scientific paper

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.

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