A Stochastic Information-Storage Model

A stochastic system that consists at time $t$ of $N_t$ automata with $n+1$ states is discussed. The states of the individual automata at time $t+1$ are obtained independently of one another in accordance with probabilities depending on the fractions of the automata in each state at time $t$. It is proved that information on the initial state of the system is retained or lost, depending on rate of growth of $N_t$.