Probability Seminars

## Asymptotics for 2D critical and near-critical first-passage percolation

### With Changlong Yao (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

# Asymptotics for 2D critical and near-critical first-passage percolation

We study Bernoulli first-passage percolation on the triangular lattice in which sites have 0 and 1 passage times with probability p and 1-p, 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 half-plane. For the supercritical phase, we give exact asymptotics for the passage times from the origin to the infinite cluster with 0-time 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 .

- Speaker: Changlong Yao (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
- Tuesday 01 May 2018, 14:00–15:00
- Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
- Series: Probability; organiser: Perla Sousi.