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We consider a Fokker–Planck equation which is coupled to an externally given time-dependent constraint on its first moment. This constraint introduces a Lagrange-multiplier which renders the equation nonlocal and nonlinear. In this paper we exploit an interpretation of this equation as a Wasserstein gradient flow of a free energy F on a time-constrained manifold. First, we prove existence of solutions by passing to the limit in an implicit Euler scheme obtained by minimizing h F ( ϱ ) + W 2 2 ( ϱ 0 , ϱ ) among all ϱ satisfying the constraint for some ϱ 0 and time-step h > 0 . Second, we provide quantitative estimates for the rate of convergence to equilibrium when the constraint converges to a constant. The proof is based on the investigation of a suitable relative entropy with respect to minimizers of the free energy chosen according to the constraint. The rate of convergence can be explicitly expressed in terms of constants in suitable logarithmic Sobolev inequalities. [ABSTRACT FROM AUTHOR]

It is usually assumed that we will need to wait until next-generation surveys like Euclid, LSST and SKA, in order to improve on the current best constraints on primordial non-Gaussianity from the Planck experiment.We show that two contemporary surveys, with the SKA precursor MeerKAT and the Dark Energy Survey (DES), can be combined using the multitracer technique to deliver an accuracy on measurement of fNL that is up to three times better than Planck. [ABSTRACT FROM AUTHOR]