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March 2006 Greedy lattice animals: Geometry and criticality
Alan Hammond
Ann. Probab. 34(2): 593-637 (March 2006). DOI: 10.1214/009117905000000693


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 Nn 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−1Nn, 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.


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Alan Hammond. "Greedy lattice animals: Geometry and criticality." Ann. Probab. 34 (2) 593 - 637, March 2006.


Published: March 2006
First available in Project Euclid: 9 May 2006

zbMATH: 1097.60081
MathSciNet: MR2223953
Digital Object Identifier: 10.1214/009117905000000693

Primary: 60K35

Keywords: lattice animals , optimization , percolation

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 2 • March 2006
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