## Large sample asymptotics of spectra of Laplacians and semilinear elliptic PDEs on random geometric graphs.

Given a data set $\mathcal{X}=\{x_1, \dots, x_n\}$ and a weighted graph structure $\Gamma= (\mathcal{X},W)$ on $\mathcal{X}$, graph based methods for learning use analytical notions like graph Laplacians, graph cuts, and Sobolev semi-norms to formulate optimization problems whose solutions serve as sensible approaches to machine learning tasks. When the data set …