# Variational formula for the time-constant of first-passage percolation

@inproceedings{Krishnan2013VariationalFF, title={Variational formula for the time-constant of first-passage percolation}, author={Arjun Krishnan}, year={2013} }

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… CONTINUE READING

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