  Supernova explosions provide the most sensitive probes of neutrino
propagation, such as the possibility that neutrino velocities might be affected
by the foamy structure of space-time thought to be generated by
quantum-gravitational (QG) effects. Recent two-dimensional simulations of the
neutrino emissions from core-collapse supernovae suggest that they might
exhibit variations in time on the scale of a few milliseconds. We analyze
simulations of such neutrino emissions using a wavelet technique, and consider
the limits that might be set on a linear or quadratic violation of Lorentz
invariance in the group velocities of neutrinos of different energies, v/c = [1
\pm (E/M_{nuLV1})] or [1 \pm (E/M_{\nuLV2})^2], if variations on such short
time scales were to be observed, where the mass scales M_{nuLVi} might appear
in models of quantum gravity. We find prospective sensitivities to M_{nuLV1} ~
2 X 10^{13} GeV and M_{nuLV2} ~ 10^6 GeV at the 95% confidence level, up to two
orders of magnitude beyond estimates made using previous one-dimensional
simulations of core-collapse supernovae. We also analyze the prospective
sensitivities to scenarios in which the propagation times of neutrinos of fixed
energies are subject to stochastic fluctuations.
