Taro Hayashi

Boundary-Moment Universality and Curvature Corrections in Random Geometric Graphs on Riemannian Manifolds

Let $(M,g)$ be a smooth, closed, connected $d$-dimensional Riemannian manifold, and let $X_1,\ldots,X_n$ be i.i.d.\ with common law $f\,d\mathrm{vol}_g$, where $f\in C^4(M)$ is strictly positive. We derive a uniform intrinsic second-order expansion for symmetric three-vertex edge-indicator statistics supported on conne...