  We study the statistics of a tagged particle in single-file diffusion, a
one-dimensional interacting infinite-particle system in which the order of
particles never changes. We compute the two-time correlation function for the
displacement of the tagged particle for an arbitrary single-file system. We
also discuss single-file analogs of the arcsine law and the law of the iterated
logarithm characterizing the behavior of Brownian motion. Using a macroscopic
fluctuation theory we devise a formalism giving the cumulant generating
functional. In principle, this functional contains the full statistics of the
tagged particle trajectory---the full single-time statistics, all multiple-time
correlation functions, etc. are merely special cases.
