Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Law of large numbers for critical first-passage percolation on the
  triangular lattice   We study the site version of (independent) first-passage percolation on the
triangular lattice $\mathbb{T}$. Denote the passage time of the site $v$ in
$\mathbb{T}$ by $t(v)$, and assume that $P(t(v)=0)=P(t(v)=1)=1/2$. Denote by
$a_{0,n}$ the passage time from $\textbf{0}$ to $(n,0)$, and by $b_{0,n}$ the
passage time from $\textbf{0}$ to the halfplane $\{(x,y):x\geq n\}$. We prove
that there exists a constant $0<\mu<\infty$ such that as $n\rightarrow\infty$,
$a_{0,n}/\log n\rightarrow \mu$ in probability and $b_{0,n}/\log n\rightarrow
\mu/2$ almost surely. This result confirms a prediction of Kesten and Zhang
(Probab. Theory Relat. Fields \textbf{107}: 137--160, 1997). The proof relies
on the existence of the full scaling limit of critical site percolation on
$\mathbb{T}$, established by Camia and Newman.

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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph