Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational formula for the time-constant of first-passage percolation   We consider first-passage percolation with positive, stationary-ergodic
weights on the square lattice $\mathbb{Z}^d$. Let $T(x)$ be the first-passage
time from the origin to a point $x$ in $\mathbb{Z}^d$. The convergence of the
scaled first-passage time $T([nx])/n$ to the time-constant as $n \to \infty$
can be viewed as a problem of homogenization for a discrete
Hamilton-Jacobi-Bellman (HJB) equation. We derive an exact variational formula
for the time-constant, and construct an explicit iteration that produces a
minimizer of the variational formula (under a symmetry assumption). We
explicitly identify when the iteration produces correctors.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom