no code implementations • 18 Aug 2017 • Braxton Osting, Todd Harry Reeb
With probability one with respect to the choice of points $\{x_i\}_{i \in \mathbb{N}}$, we show that as $n \to \infty$ the discrete Dirichlet energies for functions $G_n \to \Sigma_k$ $\Gamma$-converge to (a scalar multiple of) the continuum Dirichlet energy for functions $U \to \Sigma_k$ with respect to a metric coming from the theory of optimal transport.
