Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On pinned fields, interlacements, and random walk on $(\mathbb{Z}/N
  \mathbb{Z})^2$   We define two families of Poissonian soups of bidirectional trajectories on
$\mathbb{Z}^2$, which can be seen to adequately describe the local picture of
the trace left by a random walk on the two-dimensional torus $(\mathbb{Z}/N
\mathbb{Z})^2$, started from the uniform distribution, run up to a time of
order $(N\log N)^2$ and forced to avoid a fixed point. The local limit of the
latter was recently established in arXiv:1502.03470. Our construction proceeds
by considering, somewhat in the spirit of statistical mechanics, a sequence of
finite-volume approximations, consisting of random walks avoiding the origin
and killed at spatial scale $N$, either using Dirichlet boundary conditions, or
by means of a suitably adjusted mass. By tuning the intensity $u$ of such walks
with $N$, the occupation field can be seen to have a nontrivial limit,
corresponding to that of the actual random walk. Our construction thus yields a
two-dimensional analogue of the random interlacements model introduced in
arXiv:0704.2560 in the transient case. It also links it to the pinned free
field in $\mathbb{Z}^2$, by means of a (pinned) Ray-Knight type isomorphism
theorem.

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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys