Convergence to equilibrium for granular media equations and their Euler schemes

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Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, methodology): “Both the PDE approach in [9] and the approach based on synchronuous coupling in [11, 42] require global positive curvature bounds.”
Simulation of McKean–Vlasov SDEs with super-linear growth (2018, methodology): “[21] studies an implicit Euler scheme in order to approximate a specific equation and requires constant diffusion coefficient, symmetry and uniform convexity of the interaction potential.”
Probabilistic approach for granular media equations in the non-uniformly convex case (2006, methodology): “ even a strict convexity condition does not seem to be useful for such an approach. 4.2 Logarithmic Sobolev inequality Under a global uniform convexity condition (i.e. C= 0 in (2)), Malrieu proves in [Mal03] that the invariant measure of the centered particles system i.e. uN ∞(y)dy= Z−1 N exp − 1 2”
Mean Field Limit for Stochastic Particle Systems (2017, methodology): “If the interaction kernel K is globally Lipschitz, a standard method to show the mean field limit was popularized by Sznitman [71] (see also the more recent [58]).”
Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces (2005, unknown): “For concentration estimates in one observable, a beautiful study of these issues was performed by Malrieu [20].”