Greedy lattice animals: Geometry and criticality

Journal article

Assign to each site of the integer lattice ℤ a real score, sampled according to the same distribution F, independently of the choices made at all other sites. A lattice animal is a finite connected set of sites, with its weight being the sum of the scores at its sites. Let N n be the maximal weight of those lattice animals of size n that contain the origin. Denote by N the almost sure finite constant limit of n -1N n, which exists under a mild condition on the positive tail of F. We study certain geometrical aspects of the lattice animal with maximal weight among those contained in an n-box where n is large, both in the supercritical phase where N > 0, and in the critical case where N = 0. © Institute or Mathematical Statistics, 2006.

Authors: Hammond, A

• Publication status: Published
• Journal: ANNALS OF PROBABILITY
• Volume: 34
• Issue: 2
• Pages: 593-637
• Publication date: 2006-03-01
• DOI: 10.1214/009117905WO000693
• ISSN: 0091-1798
• Language: English
• Keywords: percolation; lattice animals; optimization