2012 / December Volume 7 No.4
On $(\mathbb Z/N\mathbb Z)^2$- Occupation Times, the Gaussian Free Field, and Random Interlacements
| Published Date |
2012 / December
|
|---|---|
| Title | On $(\mathbb Z/N\mathbb Z)^2$- Occupation Times, the Gaussian Free Field, and Random Interlacements |
| Author | |
| Keyword | |
| Download | |
| Pagination | 565-602 |
| Abstract | We study the
occupation times left by random walk on $(\mathbb Z/N\mathbb Z)^2$ at times
either proportional to $N^2 \log N$ or much larger than $N^2 \log N$, and relate these random fields to the Gaussian free field pinned at the origin. Our results answer a question raised in [18] and mirror limit statements in [18] for the occupation times of large rods of size $N$ in $\mathbb Z^3$ by random interlacements at a level $u_N$ such that $u_N N^3$ is either proportional to $N^2 \log N$ or much larger than $N^2 \log N$.
|
| AMS Subject Classification |
60J27, 60F05, 60G15
|
| Received |
2011-12-23
|
| Accepted |
2012-12-26
|