Lower bounds for critical values of a cancellative model

We consider the following one-dimensional discrete-time cancellative model whose evolution is given by eta(n+1)(x) = eta(n)(x + 1) + eta(n)(x - 1) (mo d 2) with probability p and eta(n+1) = 0 with probability 1 - p. Concerning critical probabilities p(c) and p(c)* on a survival probability, it is kno wn that 0.706 less than or equal to p(c) less than or equal to p(c)* < 1 un der a condition. In this paper, we give improved lower bounds of 0.771 and 0.781 on p(c) and p(c)*, respectively, by finding suitable supermartingales for the model.