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Interpolation is the theory of constructing smooth functions, usually polynomials or trigonometric polynomials, whose graph passes through a number of given points in the plane. Splines and Bézier curves, piecewise linear or cubic interpolation, Lagrange and Hermite interpolation are example topics.
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Wasserstein interpolation between two probability measures on a metric space
The following discussion is based on the book Gradient Flows by Ambrosio, Gigli, and Savare (2008).
Consider $p$-Wasserstein distance with $p>1$ on a Hilbert space (for the sake of uniqueness). Let $ …