  We consider the yielding behavior of amorphous solids under cyclic shear
deformation and show that it can be mapped into a random walk in a confining
potential with an absorbing boundary. The resulting dynamics is governed by the
first passage time into the absorbing state and suffices to capture the
essential qualitative features recently observed in atomistic simulations of
amorphous solids. Our results provide insight into the mechanism underlying
yielding and its robustness. When the possibility of activated escape from
absorbing states is added, it leads to a unique determination of a threshold
energy and yield strain, suggesting thereby an appealing approach to
understanding fatigue failure.
