Convergence to equilibrium for a degenerate McKean-Vlasov Equation

TL;DR

This paper investigates the convergence to equilibrium for a degenerate McKean-Vlasov equation, linking it to a linear Fokker-Planck equation and applying recent results to derive explicit convergence rates.

Contribution

It establishes a connection between nonlinear McKean-Vlasov equations and linear Fokker-Planck equations, providing sharp, computable convergence rates for degenerate cases.

Findings

Derived explicit convergence rates to equilibrium.

Linked nonlinear McKean-Vlasov solutions to linear Fokker-Planck equations.

Applied recent sharp convergence results to degenerate cases.

Abstract

In this work we study the convergence to equilibrium for a (potentially) degenerate nonlinear and nonlocal McKean-Vlasov equation. We show that the solution to this equation is related to the solution of a linear degenerate and/or defective Fokker-Planck equation and employ recent sharp convergence results to obtain an easily computable (and many times sharp) rates of convergence to equilibrium for the equation in question.