2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71296We study the asymptotic behavior of a Markov chain on $\mathbb{Z}^2$ that corresponds to the two-dimensional marginals of a reinforcement process on $\mathbb{Z}^{\mathbb{N}}$. Three distinct asymptotic regimes are identified, depending on the scaling of the reinforcement parameter $Δ$ with respect to the number of steps performed by the chain.9 pagesProbability60F05, 60J10, 60K35text