  Primordial black hole (PBH) mergers have been proposed as an explanation for
the gravitational wave events detected by the LIGO collaboration. Such PBHs may
be formed in the early Universe as a result of the collapse of extremely rare
high-sigma peaks of primordial fluctuations on small scales, as long as the
amplitude of primordial perturbations on small scales is enhanced significantly
relative to the amplitude of perturbations observed on large scales. One
consequence of these small-scale perturbations is generation of stochastic
gravitational waves that arise at second order in scalar perturbations, mostly
before the formation of the PBHs. These induced gravitational waves have been
shown, assuming gaussian initial conditions, to be comparable to the current
limits from the European Pulsar Timing Array, severely restricting this
scenario. We show, however, that models with enhanced fluctuation amplitudes
typically involve non-gaussian initial conditions. With such initial
conditions, the current limits from pulsar timing can be evaded. The amplitude
of the induced gravitational-wave background can be larger or smaller than the
stochastic gravitational-wave background from supermassive black hole binaries.
