  A Weyl semimetal is a three dimensional topological gapless phase. In the
presence of strong enough disorder it undergoes a quantum transition towards a
diffusive metal phase whose universality class depends on the range of disorder
correlations. Similar to other quantum transitions driven by disorder, the
critical wave functions at the semimetal-diffusive metal transition exhibit
multifractality. Using renormalization group methods we study the corresponding
multifractal spectrum as a function of the range of disorder correlations for
generic disorder including random scalar and vector potentials. We also discuss
the relation between the geometric fluctuations of critical wave functions and
the broad distribution of the local density of states (DOS) at the transition.
We derive a new scaling relation for the typical local DOS and argue that it
holds for other disorder-driven transitions in which both the average and
typical local DOS vanish on one side of the transition. As an illustration we
apply it to the recently discussed unconventional quantum transition in
disordered semiconductors with power-law dispersion relation near the band
edge.
