Details

Autor(en) / Beteiligte

• Grimmett, Geoffrey R.

Titel

Infinite paths in randomly oriented lattices

Ist Teil von

• Random structures & algorithms, 2001-05, Vol.18 (3), p.257-266

Ort / Verlag

New York: John Wiley & Sons, Inc

Erscheinungsjahr

2001

Link zum Volltext

Quelle

Wiley Online Library Journals Frontfile Complete

Beschreibungen/Notizen

• The square lattice is used to generate an oriented graph in which a rightward or upward arrow is present on each edge with probability a, and a leftward or downward arrow with probability b. Independence between different edges of the square lattice is assumed, but nothing is assumed concerning the dependence between the two possible orientations at any given edge. A property of self‐duality is exploited to show that, when a+b=1, the process is, in a sense to be made precise, either critical or supercritical, but not subcritical. This observation enables progress with the percolation problem in which each horizontal edge is oriented rightward with probability p and otherwise leftward, and each vertical edge is oriented upward with probability p and otherwise downward. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18, 257–266, 2001