Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interlacement limit of a stopped random walk trace on a torus   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).

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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys