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math.PR2025
Speed of Convergence and Moderate Deviations of FPP on Random Geometric Graphs
Lucas R. de Lima, Daniel Valesin
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 investig…
math.PR2024
Asymptotic Shape of Subadditive Processes on Groups and on Random Geometric Graphs
Lucas R. de Lima
This doctoral thesis undertakes an in-depth exploration of limiting shape theorems across diverse mathematical structures, with a specific focus on subadditive processes within fin…
math.PR2024
Asymptotic shape for subadditve processes on groups of polynomial growth
Cristian F. Coletti, Lucas R. de Lima
This study delves into the exploration of the limiting shape theorem for subadditive processes on finitely generated groups with polynomial growth, commonly referred to as virtuall…