  Soft solids like colloidal glasses exhibit a yield stress, above which the
system starts to flow. The microscopic analogon in microrheology is the
delocalization of a tracer particle subject to an external force exceeding a
threshold value, in a glassy host. We characterize this delocalization
transition based on a bifurcation analysis of the corresponding mode-coupling
theory equations. A schematic model is presented first, that allows analytical
progress, and the full physical model is studied numerically next. This
analysis yields a continuous type A transition with a critical power law decay
of the probe correlation functions with exponent $-1/2$. In order to compare
with simulations with a limited duration, a finite time analysis is performed,
which yields reasonable results for not-too-small wave vectors. The
theoretically predicted findings are verified by Langevin dynamics simulations.
For small wave vectors we find anomalous behavior for the probe position
correlation function, which can be traced back to a wave vector divergence of
the critical amplitude. In addition we propose and test three methods to
extract the critical force from experimental data, which provide the same value
of the critical force when applied to the finite-time theory or simulations.
