Open Access
November, 1993 Greedy Lattice Animals I: Upper Bounds
J. Theodore Cox, Alberto Gandolfi, Philip S. Griffin, Harry Kesten
Ann. Appl. Probab. 3(4): 1151-1169 (November, 1993). DOI: 10.1214/aoap/1177005277

Abstract

Let {Xν:νZd} be an i.i.d. family of positive random variables. For each set ξ of vertices of Zd, its weight is defined as S(ξ)=νξXν. A greedy lattice animal of size n is a connected subset of Zd of n vertices, containing the origin, and whose weight is maximal among all such sets. Let Nn denote this maximal weight. We show that if the expectation of Xνd(log+Xν)d+a is finite for some a>0, then w.p.1 NnMn eventually for some finite constant M. Estimates for the tail of the distribution of Nn are also derived.

Citation

Download Citation

J. Theodore Cox. Alberto Gandolfi. Philip S. Griffin. Harry Kesten. "Greedy Lattice Animals I: Upper Bounds." Ann. Appl. Probab. 3 (4) 1151 - 1169, November, 1993. https://doi.org/10.1214/aoap/1177005277

Information

Published: November, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0818.60039
MathSciNet: MR1241039
Digital Object Identifier: 10.1214/aoap/1177005277

Subjects:
Primary: 60G50
Secondary: 60K35

Keywords: lattice animals , optimization , self-avoiding paths , Spanning trees

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.3 • No. 4 • November, 1993
Back to Top