We studied supernova neutrino oscillations in the presence of self-interactions that induce collective flavor transitions. For the chosen matter profile, collective transitions are decoupled from matter oscillations, allowing for the analytical interpretation of the numerical simulations. Of particular interest is the case of inverted neutrino hierarchy, where neutrino propagation can be divided in three regimes, of synchronized and bipolar oscillations, and then of spectral split. Our simulation shows that averaging over neutrino trajectories does not alter the nature of these three regimes, apart from the smearing of fine structure details.
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