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arXiv · 2411.02046

Speed of Convergence and Moderate Deviations of FPP on Random Geometric Graphs

Lucas R. de Lima·Daniel Valesin
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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.

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Lucas R. de Lima, Daniel Valesin. 2024-11-04. Speed of Convergence and Moderate Deviations of FPP on Random Geometric Graphs. https://doi.org/10.1016/j.spa.2025.104652

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