It has been speculated that Lorentz-invariance violation (LIV) might be
generated by quantum-gravity (QG) effects. As a consequence, particles may not
travel at the universal speed of light. In particular, superluminal
extragalactic neutrinos would rapidly lose energy via the bremssthralung of
electron-positron pairs (nu -> nu e+ e-), damping their initial energy into
electromagnetic cascades, a figure constrained by Fermi-LAT data. We show that
the two cascade neutrino events with energies around 1 PeV recently detected by
IceCube -if attributed to extragalactic diffuse events, as it appears likely-
can place the strongest bound on LIV in the neutrino sector, namely delta
=(v^2-1) ~
10^(-4) M_Pl) for a linear (quadratic) LIV, at least for models inducing
superluminal neutrino effects (delta > 0).Comment: 4 page