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The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a deterministic ...

We consider two-dimensional Schrödinger equations with honeycomb potentials and slow time-periodic forcing of the form $i\psi_t (t,{x}) = H^\varepsilon(t)\psi=\left(H^0+2i\varepsilon A (\varepsilon t) \cdot \nabla \right)\psi, H^0=-\Delta +V ({x})$. The ...

Let $f: (0,1)^d \rightarrow \mathbb{R}$ be a continuous function with zero mean and interpret $f_{+} = \max(f, 0)$ and $f_{-} = -\min(f, 0)$ as the densities of two measures. We prove that if the cost of transport from $f_{+}$ to $f_{-}$ is small, in ...