Greedy lattice animals: geometry and criticality (with an Appendix)
| dc.creator | Hammond, Alan | |
| dc.date | 2004-11-21 | |
| dc.date.accessioned | 2026-07-07T05:14:33Z | |
| dc.date.available | 2026-07-07T05:14:33Z | |
| dc.description | Assign to each site of the integer lattice $\Zd$ 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 $n^{-1} N_n$, 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 $N = 0$. | |
| dc.description | 46 pages. Contains submitted paper, as well as an appendix. In the appendix, greedy lattice animals of constrained size are studied, and an alternative proof of Theorem 1.3 is given | |
| dc.identifier | https://arxiv.org/abs/math/0411459 | |
| dc.identifier | http://arxiv.org/abs/math/0411459 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73313 | |
| dc.subject | Probability | |
| dc.title | Greedy lattice animals: geometry and criticality (with an Appendix) | |
| dc.type | text |