2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136643We discuss a model for the autocatalytic reaction $A+B\to 2A$ on substrates where the reactants perform a compact exploration of the space, i.e., on lattices whose spectral dimension $\tilde{d}$ is $< 2$. For finite systems, the total time $τ$ for the reaction to end scales according to two different regimes, for high and low concentrations of reactants. The functional dependence of $τ$ on the volume of the substrate and the concentration of reactants is discussed within a mean-field approximation. Possible applications are discussed.15 pagesStatistical Mechanicstext