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

Author(s)

de Lima, Lucas R. ; Valesin, Daniel

• Document type: Journal article
• Source: Stochastic Processes and their Applications; v. 187, p. 23-pg., 2025-04-24.

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. (AU)

• FAPESP's process: 19/19056-2 - Asymptotic shape for subadditive processes on groups and on random geometric graphs
• Grantee: Lucas Roberto de Lima
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 24/06021-4 - Growth models subject to catastrophes and dispersion in varying and random environments
• Grantee: Lucas Roberto de Lima
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 20/12868-9 - Limiting shape for the contact process on random geometric graphs
• Grantee: Lucas Roberto de Lima
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate