2012 / December Volume 7 No.4
On $(\mathbb Z/N\mathbb Z)^2$- Occupation Times, the Gaussian Free Field, and Random Interlacements
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2012 / December
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Title | On $(\mathbb Z/N\mathbb Z)^2$- Occupation Times, the Gaussian Free Field, and Random Interlacements |
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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 $N^2 \log N$.
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AMS Subject Classification |
60J27, 60F05, 60G15
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Received |
2011-12-23
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Accepted |
2012-12-26
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