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We study a class of reflected McKean-Vlasov diffusions over a convex domainwith self-stabilizing coefficients. This includes coefficients that do notsatisfy the classical Wasserstein Lipschitz condition. Further, the process isconstrained to a (not necessarily bounded) convex domain by a local time on theboundary. These equations include the subclass of reflected self-stabilizingdiffusions that drift towards their mean via a convolution of the solution lawwith a stabilizing potential.  Firstly, we establish existence and uniqueness results for this class andaddress the propagation of chaos. We work with a broad class of coefficients,including drift terms that are locally Lipschitz in spatial and measurevariables. However, we do not rely on the boundedness of the domain or thecoefficients to account for these non-linearities and instead use theself-stabilizing properties.  We prove a Freidlin-Wentzell type Large Deviations Principle and anEyring-Kramer's law for the exit-time from subdomains contained in the interiorof the reflecting domain.

Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts