Lower bounds for critical values of a cancellative model
Norio Konno; Kazunori Sato; Aidan Sudbury
Журнал:
Journal of Physics A: Mathematical and General
Дата:
2000-01-21
Аннотация:
We consider the following one-dimensional discrete-time cancellative model whose evolution is given by <sub>n +1</sub> (x ) = <sub>n</sub> (x +1)+ <sub>n</sub> (x -1) (mod 2) with probability p and <sub>n +1</sub> = 0 with probability 1-p . Concerning critical probabilities p<sub>c</sub> and p<sub>c</sub> * on a survival probability, it is known that 0.706 p<sub>c</sub> p<sub>c</sub> *<1 under a condition. In this paper, we give improved lower bounds of 0.771 and 0.781 on p<sub>c</sub> and p<sub>c</sub> *, respectively, by finding suitable supermartingales for the model.
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