A Note on a Problem by Welsh in First-Passage Percolation
by
Sven Erick Alm
Uppsala University
In Combinatorics, Probability and Computing (1998) 7, 11-15
Abstract
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.