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math.PR2026
The probability of connection between two vertices cannot be monotone with the distance for Bernoulli Percolation on transitive graphs
Alberto M. Campos, Bernardo N. B. de Lima
A popular question in Bernoulli percolation models is if the probability of connection between two vertices in a transitive graph decays monotonically with the distance between the…
math.PR2025
Hydrodynamic limit for repeated averages on the complete graph
Alberto M. Campos, Tertuliano Franco, Markus Heydenreich +1
We establish a hydrodynamical limit for the averaging process on the complete graph with N vertices, showing that, after a timescale of order N, the empirical distribution of opini…
math.PR2024
First order of the renewal covering of the natural numbers
Alberto M. Campos
This paper introduces a new type of covering process that covers the set of natural numbers using renewal processes as objects. Inspired by the behavior of prime numbers, the model…