Speed of convergence and moderate deviations of FPP on random geometric graphs

Lucas R. de Lima and Daniel Valesin

Stochastic Processes and their Applications, 2025, vol. 187, issue C

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: First-passage percolation; Random geometric graphs; Quantitative shape theorem; Moderate deviations; Spanning trees; Stochastic processes (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104652

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