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

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.

35 pages, 5 figures, Theorems 1.4 and 1.5 reformulated in the latest version

References in corpus (5)

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