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Bernoulli percolation, infinite path from (0,0) in a "cone"

Look at Bernoulli percolation on $\mathbb{Z}^2$ with $p> p_c$ ($p$ can be arbitrarily close to 1). …
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3 votes
0 answers
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super-critical percolation on $\mathbb{Z}^2$, number of corners in a directed open path

Define the planar percolation where each unit edge is open with probability $p$ very close to $1$. Looking at the event where there exists a directed open path between $(0,0)$ and $(n,n)$. … Is there a reference for this type of problem in percolation theory? …
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