Abstract: 

Consider Bernoulli first-passage percolation on the triangular lattice in which sites have 0 and 1 passage times with probability p and 1-p, respectively. First, I will discuss a result in the subcritical regime. Let B(p) be the limit shape in the classical shape theorem, and let L(p) be the correlation length. I will show that the re-scaled limit shape B(p)/L(p) converges to a Euclidean disk, as p tends to p_c from below. The proof relies on the renormalization argument, the scaling limit of near-critical percolation and the construction of the collection of continuum clusters. Then, I will review some recent results and problems in the critical and near-critical cases.

Tencent Information

Link: https://meeting.tencent.com/dm/lzlJkpJxE3db

ID: 533-901-844

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