## Journal of Mathematics of Kyoto University

### A note on anisotropic first-passage percolation

Masato Takei

#### Abstract

We consider a first-passage percolation problem on the square lattice, where the distribution function of time coordinates of horizontal edges may be different from that of vertical edges. Some basic limit theorems for first-passage times and minimal lengths of optimal paths are obtained. Especially, we show that as long as the system is in the supercritical phase, the expectation of first-passage time from the origin to a point with distance $n$ converges to a finite constant, which is independent of the directions, as $n \to \infty$.

#### Article information

Source
J. Math. Kyoto Univ., Volume 46, Number 4 (2006), 903-912.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281609

Digital Object Identifier
doi:10.1215/kjm/1250281609

Mathematical Reviews number (MathSciNet)
MR2320356

Zentralblatt MATH identifier
1137.60348

#### Citation

Takei, Masato. A note on anisotropic first-passage percolation. J. Math. Kyoto Univ. 46 (2006), no. 4, 903--912. doi:10.1215/kjm/1250281609. https://projecteuclid.org/euclid.kjm/1250281609