On cover times for 2D lattices
On cover times for 2D lattices
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二维晶格的覆盖时间
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发表时间：
2011
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通讯作者：
Jian Ding
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作者：
Jian Ding
我们研究了在边长为$n$的有线边界的二维盒子上和二维环面上通过（连续时间）随机游动的覆盖时间$ au_{mathm {cov}}$，并证明了在这两种情况下，随着$n$的增加，概率接近$1$,$sqrt{au_{mathm {cov}}}=sqrt{2n^2 [sqrt{2/pi} log n + O(loglog n)]$。这改进了Dembo、Peres、Rosen和Zeitouni（2004）的结果，并向Bramson和Zeitouni（2009）的猜想迈进了一步。
We study the cover time $ au_{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,$sqrt{ au_{mathrm{cov}}}=sqrt{2n^2 [sqrt{2/pi} log n + O(loglog n)]$. This improves a result of Dembo, Peres, Rosen, and Zeitouni (2004) and makes progresstowards a conjecture of Bramson and Zeitouni (2009).