5 papers
Infinite-dimensional genetic and evolution algebras generated by Gibbs measures
Cristian F. Coletti, Lucas R. de Lima, Denis A. Luiz
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and…
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…
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…
Generic spectrum of the weighted Laplacian operator on Cayley graphs
Cristian F. Coletti, Lucas R. de Lima, Diego S. de Oliveira +1
In this paper, we investigate the spectrum of a class of weighted Laplacians on Cayley graphs and determine under what conditions the corresponding eigenspaces are generically irre…
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…