## Seminars

## Seminars

## Probability and Statistics Seminar——Convergence of limit shapes for 2D near-critical first-passage percolation

**Holder：** Changlong Yao (CAS)

**Time：**2022-05-30 14:00-15:00

**Location：**Tencent Meeting（533-901-844）

**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.

**About the Speaker: **

姚昌龙于2011年获中国科学院大学博士学位，现为中国科学院数学与系统科学研究院助理研究员。

homepage：*http://homepage.amss.ac.cn/research/homePage/fb0912e04e774e689a285f7a71fdd815/myHomePage.html*

Tencent Information Link: *https://meeting.tencent.com/dm/lzlJkpJxE3db*

ID: 533-901-844

Password: 123456

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