8 citations · 13 across the 9 of their papers we have counts for
9 papers
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…
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…
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…
Limiting shape for First-Passage Percolation models on Random Geometric Graphs
Cristian F. Coletti, Lucas R. de Lima, Alexander Hinsen +2
Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percol…
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…
Limit theorems for a random walk with memory perturbed by a dynamical system
Cristian F. Coletti, Lucas R. de Lima, Renato J. Gava +1
We introduce a new random walk with unbounded memory obtained as a mixture of the Elephant Random Walk and the Dynamic Random Walk which we call the Dynamic Elephant Random Walk (D…
Limit theorems for a minimal random walk model
Cristian F Coletti, Lucas R de Lima, Renato Gava
We study the minimal random walk introduced by Kumar, Harbola and Lindenberg. It is a random process on with unbounded memory which exhibits subdiffusive, diffu…
The asymptotic shape theorem for the frog model on finitely generated abelian groups
Cristian F. Coletti, Lucas R. de Lima
We study the frog model on Cayley graphs of groups with polynomial growth rate . The frog model is an interacting particle system in discrete time. We consider that the p…