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Oriented site percolation, phase transitions and probability bounds. (English) Zbl 1087.60075
There are few exact results for computing critical probability in site percolation or oriented percolation. In this paper, a simple lemma is used to prove a result of J. Bishir [J. R. Stat. Soc., Ser. B 25, 401–404 (1963; Zbl 0123.35804)] stating that the critical probability for the one-quadrant oriented percolation is bounded below by 2/3. The same lemma is used to improve the known lower bound of one third for the critical probability of another oriented site percolation process. The new bound is one half, whereas Monte Carlo simulation indicates a critical value close to 0.535.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
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