Greedy lattice animals: Geometry and criticality
成果类型：
Article
署名作者：
Hammond, Alan
署名单位：
University of California System; University of California Berkeley
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117905000000693
发表日期：
2006
页码：
593-637
关键词：
摘要：
Assign to each site of the integer lattice Z(d) 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 if that contain the origin. Denote by N the almost sure finite constant limit of n(-1) N-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.