Linear growth for greedy lattice animals

James B. Martin

Stochastic Processes and their Applications, 2002, vol. 98, issue 1, 43-66

Abstract: Let d[greater-or-equal, slanted]2, and let be an i.i.d. family of non-negative random variables with common distribution F. Let N(n) be the maximum value of [summation operator]v[set membership, variant][xi]Xv over all connected subsets [xi] of of size n which contain the origin. This model of "greedy lattice animals" was introduced by Cox et al. (Ann. Appl. Probab. 3 (1993) 1151) and Gandolfi and Kesten (Ann. Appl. Probab. 4 (1994) 76), who showed that if for some [var epsilon]>0, then N(n)/n-->N a.s. and in for some N

Keywords: Lattice; animals; Self-avoiding; paths; Superadditivity; Concentration; inequality (search for similar items in EconPapers)
Date: 2002
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