  The density of states of a three dimensional Dirac equation with a random
potential as well as in other problems of quantum motion in a random potential
placed in sufficiently high spatial dimensionality appears to be singular at a
certain critical disorder strength. This was seen numerically in a variety of
studies as well as supported by detailed renormalization group calculations. At
the same time it was suggested by a number of arguments accompanied by detailed
numerical simulations that this singularity is rounded off by the rare region
fluctuations of random potential, and that tuning the disorder past its
critical value is not a genuine phase transition but rather a crossover. Here
we develop an analytic theory which explains how rare region effects indeed
lead to rounding off of the singularity and to the crossover replacing the
transition.
