Optimal Transport: Heat Equation and Metric Spaces

Related lectures (30)

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Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Covers topics in probability theory, focusing on uniform integrability and convergence theorems.

Covers the concept of outer measure and properties of measurable sets.

Explores optimal transport theory with a focus on heat equations and Wasserstein distance.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Explores implicit schemes in numerical analysis, emphasizing stability and convergence properties in solving differential equations.

Covers stability in optimal transport and provides examples of discontinuous optimal solutions.