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

  • Authors:

  • Sven Erick Alm

  • Affiliations:

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

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 1998

Quantified Score

Hi-index 0.00

Visualization

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.