Speed of Convergence and Moderate Deviations of FPP on Random Geometric Graphs
Probability
2025-04-28 v2
Abstract
This study delves into first-passage percolation on random geometric graphs in the supercritical regime, where the graphs exhibit a unique infinite connected component. We investigate properties such as geodesic paths, moderate deviations, and fluctuations, aiming to establish a quantitative shape theorem. Furthermore, we examine fluctuations in geodesic paths and characterize the properties of spanning trees and their semi-infinite paths.
Keywords
Cite
@article{arxiv.2411.02046,
title = {Speed of Convergence and Moderate Deviations of FPP on Random Geometric Graphs},
author = {Lucas R. de Lima and Daniel Valesin},
journal= {arXiv preprint arXiv:2411.02046},
year = {2025}
}
Comments
35 pages, 5 figures, Theorems 1.4 and 1.5 reformulated in the latest version