Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-17T20:39:53.087Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  01 March 1998

Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden


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.

Research Article
1998 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)