  Single-file diffusion is a theoretically challenging many-body problem where
the calculation of even the simplest observables, e.g. mean square
displacement, for a tracer particle requires a heavy mathematical machinery.
There is therefore a need for simple approaches which predict qualitatively
correct behaviours. Here we put forward one such method which we use to
investigate the influence of non-thermal initial conditions on the dynamics of
a tracer particle. With our new approach we reproduce, up to scaling, several
known asymptotic results for the tracer particle mean square displacement.
