A Note on a Problem by Welsh in First-Passage Percolation


Sven Erick Alm

Uppsala University

In Combinatorics, Probability and Computing (1998) 7, 11-15


Consider first-passage percolation on the square lattice. Welsh, who together with Hammersley introduced the subject in 1963, has formulated a problem about mean first-passage times, which, although seemingly simple, has not been proved in any non-trivial case. In this paper we give a general proof of Welsh's problem.

1998-04-07, Sven Erick Alm, sea@math.uu.se