A particle in a one-dimensional channel with excluded volume interaction displays anomalous single-file diffusion with fluctuations scaling as t^(1/4) in the long time limit. This phenomenon has been demonstrated in various experiments involving different types of physical systems such as zeolites, capillary pores, carbon nanotubes or colloids. On a one dimensional lattice, the Symmetric Exclusion Process, particles performing symmetric random walks and interacting by hard-core exclusion, is a pristine model of a single-file diffusion, amenable to quantitative analysis (Spitzer, 1970). At equilibrium, the variance of the position of a tagged particle has been calculated exactly by Arratia in 1983, and this result has been discussed since then in numerous theoretical papers, at various levels of physical intuition or mathematical rigor. However, the full distribution of a tagged particle and its higher cumulants (prone to experimental measurements) are not known. A rigorous work by S.
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