For the spectral regularization of Dean-Kawasaki, superpolynomial weak convergence to N-particle empirical measures holds if and only if the initial density is bounded away from zero; otherwise only polynomial rates are possible.
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On the role of positivity preservation for high order approximations of the Dean--Kawasaki equation
For the spectral regularization of Dean-Kawasaki, superpolynomial weak convergence to N-particle empirical measures holds if and only if the initial density is bounded away from zero; otherwise only polynomial rates are possible.