Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization for random walks among random obstacles in a single
  Euclidean ball   Place an obstacle with probability $1-p$ independently at each vertex of
$\mathbb Z^d$, and run a simple random walk until hitting one of the obstacles.
For $d\geq 2$ and $p$ strictly above the critical threshold for site
percolation, we condition on the environment where the origin is contained in
an infinite connected component free of obstacles, and we show that for
environments with probability tending to one as $n\to \infty$ there exists a
unique discrete Euclidean ball of volume $d \log_{1/p} n$ asymptotically such
that the following holds: conditioned on survival up to time $n$ we have that
at any time $t \in [o(n),n]$ with probability tending to one the simple random
walk is in this ball. This work relies on and substantially improves a previous
result of the authors on localization in a region of volume poly-logarithmic in
$n$ for the same problem.

9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg