Skip to main content Accessibility help

First-passage percolation processes with finite height

  • Norbert Herrndorf (a1)


We consider first-passage percolation in an infinite horizontal strip of finite height. Using methods from the theory of Markov chains, we prove a central limit theorem for first-passage times, and compute the time constants for some special cases.


Corresponding author

Postal address: Mathematisches Institut der Universität Köln, Weyerthal 86–90, D-5000 Köln 41, West Germany.


Hide All
Cox, J. T. (1980) The time constant of first-passage percolation on the square lattice. Adv. Appl. Prob. 12, 864879.
Dobrushin, R. L. (1956) Central limit theorem for nonstationary Markov chains. Theory Prob. Appl. 1, 6580; 329-383.
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.
Hammersley, J. M. and Welsh, D. J. A. (1965) First passage percolation, subadditive processes, stochastic networks, and generalized renewal theory. In Bernoulli-Bayes-Laplace Anniversary Volume , ed. Neyman, J. and LeCam, L. M., Springer-Verlag, Berlin.
Ibragimov, I. A. (1962) Some limit theorems for stationary processes. Theory Prob. Appl. 7, 349382.
Iosifescu, M. and Theodorescu, R. (1969) Random Processes and Learning. Springer-Verlag, Berlin.
Kingman, J. F. C. (1968) The ergodic theory of subadditive stochastic processes. J. R. Statist. Soc. B 30, 499510.
Smythe, R. T. and Wierman, J. C. (1978) First Passage Percolation on the Square Lattice. Lecture Notes in Mathematics 671, Springer-Verlag, Berlin.
Wierman, J. C. (1982) Percolation theory. Ann. Prob. 10, 509524.


First-passage percolation processes with finite height

  • Norbert Herrndorf (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed