  We present a toy charge density wave (CDW) model in 1d exhibiting a depinning
transition with threshold force and configurations that are explicit. Due to
the periodic boundary conditions imposed, the threshold configuration has a set
of topological defects whose location and number depend on the realization of
the random phases. Approaching threshold, these defects are relocated by
avalanches whose size dependence on the external driving force $F$ is described
by a record-breaking process. We find that the depinning transition in this
model is a critical phenomenon, with the cumulative avalanche size diverging
near threshold as $(F_{\rm th} - F)^{-2}$. The exact avalanche size
distributions and their dependence on the control parameter $(F_{\rm th} - F)$
are obtained. Remarkably, the scaling exponents associated with the critical
behavior depend on (1) the initial conditions and (2) the relationship between
the system size and the pinning strength.
