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• W1878423399 abstract "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." @default.
• W1878423399 created "2016-06-24" @default.
• W1878423399 creator A5010363470 @default.
• W1878423399 date "2013-11-01" @default.
• W1878423399 modified "2023-09-27" @default.
• W1878423399 title "Variational formula for the time-constant of first-passage percolation" @default.
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• W1878423399 hasPublicationYear "2013" @default.
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