The stability of the MSW solution to the solar neutrino problem with respect to random matter density perturbations

We present a generalization of the resonant neutrino conversion in matter, including a random component in the matter density profile. The study is focused on the effect of such matter perturbations upon both large and small mixing angle MSW solutions to the solar neutrino problem. This is carried out both for the active-active $\nu_e \ra \nu_{\mu,\tau}$ as well as active-sterile $\nu_e \ra \nu_s$ conversion channels. We find that the small mixing MSW solution is much more stable (especially in $\delta m^2$) than the large mixing solution. Future solar neutrino experiments, such as Borexino, could probe solar matter density noise at the few percent level.