Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-point correlations for two dimensional coalescing random walks   This paper considers an infinite system of instantaneously coalescing rate
one simple random walks on $\mathbb{Z}^2$, started from the initial condition
with all sites in $\mathbb{Z}^2$ occupied. We show that the correlation
functions of the model decay, for any $N \geq 2$, as \[ \rho_N
(x_1,\ldots,x_N;t) = \frac{c_0(x_1,\ldots,x_N)}{\pi^N} (\log t)^{N-{N \choose
2}} t^{-N} \left(1 + O\left( \frac{1}{\log^{\frac12-\delta}\!t} \right) \right)
\] as $t \to\infty$. This generalises the results for $N=1$ due to Bramson and
Griffeath and confirms a prediction in the physics literature for $N>1$. An
analogous statement holds for instantaneously annihilating random walks.
  The key tools are the known asymptotic $\rho_1(t) \sim \log t/\pi t$ due to
Bramson and Griffeath, and the non-collision probability $p_{NC}(t)$, that no
pair of a finite collection of $N$ two dimensional simple random walks meets by
time $t$, whose asymptotic $p_{NC}(t) \sim c_0 (\log t)^{-{N \choose 2}}$ was
found by Cox, Merle and Perkins. This paper re-derives the asymptotics both for
$\rho_1(t)$ and $p_{NC}(t)$ by proving that these quantities satisfy {\it
effective rate equations}, that is approximate differential equations at large
times. This approach can be regarded as a generalisation of the Smoluchowski
theory of renormalised rate equations to multi-point statistics.

20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph