  Single-file diffusion refers to the motion of diffusive particles in narrow
channels, so that they cannot bypass each other. This constraint leads to the
subdiffusion of a tagged particle, called the tracer. This anomalous behaviour
results from the strong correlations that arise in this geometry between the
tracer and the surrounding bath particles. Despite their importance, these
bath-tracer correlations have long remained elusive, because their
determination is a complex many-body problem. Recently, we have shown that, for
several paradigmatic models of single-file diffusion such as the Simple
Exclusion Process, these bath-tracer correlations obey a simple exact closed
equation. In this paper, we provide the full derivation of this equation, as
well as an extension to another model of single-file transport: the double
exclusion process. We also make the connection between our results and the ones
obtained very recently by several other groups, and which rely on the exact
solution of different models obtained by the inverse scattering method.
