Lower and Upper Bounds for the Time Constant of First-Passage Percolation
Sven Erick Alm and Robert Parviainen
U.U.D.M. Report 2001:16, ISSN 1101-3591
In Combinatorics, Probability and Computing (2002) 11, 433-445
We present improved lower and upper bounds for the time constant of first-passage percolation on the square lattice. For the case of lower bounds, a new method, using the idea of a transition matrix, has been used. Numerical results for the exponential and uniform distributions are presented. A simulation study is included, which results in new estimates and improved confidence limits of the time constants.