  We analyze strong and weak thermalization regimes from a perspective of
rigorous mathematical upper bounds on the equilibration of isolated quantum
systems. We show that weak equilibration can be understood to be due to the
small effective dimension of the initial state. Furthermore, analyzing the
scaling of an upper bound on the fluctuations, we show that the observable
fluctuations decay exponentially with the system size for both weak and strong
thermalization indicating no sharp transitions between these two regimes.
