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- W3197110231 abstract "We consider a simple random walk on $mathbb{Z}^d$ started at the origin and stopped on its first exit time from $(-L,L)^d cap mathbb{Z}^d$. Write $L$ in the form $L = m N$ with $m = m(N)$ and $N$ an integer going to infinity in such a way that $L^2 sim A N^d$ for some real constant $A > 0$. Our main result is that for $d ge 3$, the projection of the stopped trajectory to the $N$-torus locally converges, away from the origin, to an interlacement process at level $A d sigma_1$, where $sigma_1$ is the exit time of a Brownian motion from the unit cube $(-1,1)^d$ that is independent of the interlacement process. The above problem is a variation on results of Windisch (2008) and Sznitman (2009)." @default.
- W3197110231 created "2021-09-13" @default.
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- W3197110231 date "2021-08-28" @default.
- W3197110231 modified "2023-09-27" @default.
- W3197110231 title "Interlacement limit of a stopped random walk trace on a torus" @default.
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- W3197110231 doi "https://doi.org/10.48550/arxiv.2108.12629" @default.
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