Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Has it been proved that the two dimensional semi-oriented percolation process exhibits a phase transition at $p_c < 1/2$ (STRICTLY less than 1/2!!)?

Semi-oriented Percolation: 2 dimensional lattice, where each edge directed on the right, on the left or up can be open with probability $p$ and closed with probability $(1 - p)$. The edge directed down is always closed. $\Theta(p)$ is the probability that the origin of the lattice is contained in an infinite cluster of vertices connected by open edges. $p_c$ is the sup of the values of p such that $\Theta(p)=0$.

1) $p_c \geq 1/2$ comes authomatically from the comparison with the standard percolation process.

2) for the oriented percolation (only the edges in directions up and right can be open, the 2 others are surely closed) it is proved that $p_c > 1/2$.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.