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We consider random boolean cellular automata on the integer lattice, i.e.,the cells are identified with the integers from 1 to $N$. The behaviour of theautomaton is mainly determined by the support of the random variable thatselects one of the sixteen possible Boolean rules, independently for each cell.A cell is said to stabilize if it will not change its state anymore after sometime. We classify the random boolean automata according to the positivity oftheir probability of stabilization. Here is an example of a consequence of ourresults: if the support contains at least 5 rules, then asymptotically as $N$tends to infinity the probability of stabilization is positive, whereas thereexist random boolean cellular automata with 4 rules in their support for whichthis probability tends to 0.

Stability in random Boolean cellular automata on the integer lattice