Asymptotics for 2D critical and nearcritical firstpassage percolation
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We study Bernoulli firstpassage percolation on the triangular lattice in which sites have 0 and 1 passage times with probability p and 1p, respectively. At p=1/2, we obtain explicit limit theorems for the point to point passage times a_{0,n} and the passage times between boundary points of the upper halfplane. For the supercritical phase, we give exact asymptotics for the passage times from the origin to the infinite cluster with 0time sites, as p tending to 1/2. The proof relies on the convergence of the percolation exploration path to SLE , and the collection of interface loops to CLE .
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