Abstract
We study the cover time $\tau_{\mathrm{cov}}$ by (continuous-time) random walk on the 2D box of side length $n$ with wired boundary or on the 2D torus,and show that in both cases with probability approaching $1$ as $n$ increases, $\sqrt{\tau_{\mathrm{cov}}}=\sqrt{2n^2} \left[\sqrt{2/\pi} \log n + O(\log\log n)\right]$. This improves a result of Dembo, Peres, Rosen, and Zeitouni (2004) and makes progresstowards a conjecture of Bramson and Zeitouni (2009).
Citation
Jian Ding. "On cover times for 2D lattices." Electron. J. Probab. 17 1 - 18, 2012. https://doi.org/10.1214/EJP.v17-2089
Information
