On the continuity of the time constant of first-passage percolation
- 1 December 1981
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 18 (4) , 809-819
- https://doi.org/10.2307/3213056
Abstract
LetUbe the distribution function of the non-negative passage time of an individual edge of the square lattice, and leta0nbe the minimal passage time from (0, 0) to (n, 0). The processa0n/nconverges in probability asn→ ∞to a finite constantμ(U) called the time constant. It is proven thatμ(Uk)→ μ(U) wheneverUkconverges weakly toU.Keywords
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