Connections between continuous and discrete worlds tend to be elusive. One example is
curvature. Even though there exist numerous nonequivalent definitions of graph curvature …

Roadmaps constructed by many sampling-based motion planners coincide, in the absence
of obstacles, with standard models of random geometric graphs (RGGs). Those models have …

Let $\mathcal {M}\subseteq\mathbb {R}^ d $ denote a low-dimensional manifold and let
$\mathcal {X}=\{x_1,\dots, x_n\} $ be a collection of points uniformly sampled from $\mathcal …

In this paper, we study a graph parameter that was recently introduced, the burning number,
focusing on a few probabilistic aspects of the problem. The original burning number is …

Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph
infinity Laplacian Page 1 The Annals of Applied Probability 2024, Vol. 34, No. 4, 3870–3910 …

We analyze the convergence properties of Fermat distances, a family of density-driven
metrics defined on Riemannian manifolds with an associated probability measure. Fermat …

We analyze the convergence properties of Fermat distances, a family of density-driven
metrics defined on Riemannian manifolds with an associated probability measure. Fermat …

Curvature is a fundamental geometric characteristic of smooth spaces. In recent years
different notions of curvature have been developed for combinatorial discrete objects such …

A cornerstone of machine learning is the identification and exploitation of structure in high‐
dimensional data. While classical approaches assume that data lies in a high‐dimensional …

The Price model, the directed version of the Barabási–Albert model, produces a growing
directed acyclic graph. We look at variants of the model in which directed edges are added …