Speaker：Lujing Huang (Fujian Normal University)

Time：2026-10-11 10: 00

Location：Conference Room C610 at Administration Building at Haiyun Campus

Abstract:

Consider critical long-range percolation on $\mathds{Z}$, where an edge connects $i$ and $j$ independently with probability $1-\exp\{-\beta\int_i^{i+1}\int_j^{j+1}|u-v|^{-2}\d u\d v\}$ for $|i-j|>1$ for some fixed $\beta>0$ and with probability 1 for $|i-j|=1$.

We prove that the effective resistance has a polynomial growth and both the quenched and annealed spectral dimensions of the associated simple random walk are $2/(1+\delta)$. This is based on a joint work with Jian Ding and Zherui Fan.