2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/40788The erraticity in the random-cascading $α$ model is revisited. It is found that in contrary to the previous expectation, even in the pure single-$α$ random-cascading model without putting in any particle there exists erraticity behavior and the corresponding entropy indices do not vanish. This means that the dynamical fluctuations in a pure single-$α$ model already fluctuate event-by-event. Models with multiple-$α$ strengthen this fluctuation. Taking double-$α$ model as example, the variation of the event-space fluctuation strength with the mixing ratio of the two $α$'s is studied in some detail. The influence of particle number on the results when particles are putted into the system is also investigated.8 pages, 5 figuresHigh Energy Physics - Phenomenologytext