Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit theorems for critical first-passage percolation on the triangular
  lattice   Consider (independent) first-passage percolation on the sites of 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
$b_{0,n}$ the passage time from 0 to the halfplane
$\{v\in\mathbb{T}:\mbox{Re}(v)\geq n\}$, and by $T(0,nu)$ the passage time from
0 to the nearest site to $nu$, where $|u|=1$. We prove that as
$n\rightarrow\infty$, $b_{0,n}/\log n\rightarrow 1/(2\sqrt{3}\pi)$ a.s.,
$E[b_{0,n}]/\log n\rightarrow 1/(2\sqrt{3}\pi)$ and Var$[b_{0,n}]/\log
n\rightarrow 2/(3\sqrt{3}\pi)-1/(2\pi^2)$; $T(0,nu)/\log n\rightarrow
1/(\sqrt{3}\pi)$ in probability but not a.s., $E[T(0,nu)]/\log n\rightarrow
1/(\sqrt{3}\pi)$ and Var$[T(0,nu)]/\log n\rightarrow 4/(3\sqrt{3}\pi)-1/\pi^2$.
This answers a question of Kesten and Zhang (1997) and improves our previous
work (2014). From this result, we derive an explicit form of the central limit
theorem for $b_{0,n}$ and $T(0,nu)$. A key ingredient for the proof is the
moment generating function of the conformal radii for conformal loop ensemble
CLE$_6$, given by Schramm, Sheffield and Wilson (2009).

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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph