Quantum scalar field propagator in a stochastic gravitational plane wave

A stochastic metric can appear in classical as well as in quantum gravity. We show that if the linearized stochastic Gaussian gravitational plane wave has the frequency spectrum ${\omega }^{4\gamma -1}$ ($0\le \gamma <1$) then the equal-time propagator of the scalar field behaves as $p^{-\frac{1}{1-\gamma }}$for large momenta. We discuss models of quantum field theory where such anomalous behaviour can appear.