Lifetime for certain chemical systems at criticality

We consider an autocatalytic chemical system which is exactly at criticality so that the absorbing state lies on the boundary corresponding to the extinction of a species. The average time to reach the absorbing state depends strongly on the distance from the initial state to the boundary and grows like the square root of the volume. It can be estimated in generic critical situations. These results are verified explicitly on an example, for which a direct calculation can be done.