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Linear growth for greedy lattice animals

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  • Martin, James B.

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

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  • Martin, James B., 2002. "Linear growth for greedy lattice animals," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 43-66, March.
    • Handle: RePEc:eee:spapps:v:98:y:2002:i:1:p:43-66
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    References listed on IDEAS

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    1. Lee, Sungchul, 1997. "The power laws of M and N in greedy lattice animals," Stochastic Processes and their Applications, Elsevier, vol. 69(2), pages 275-287, September.
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    Cited by:

    1. Sergey Foss & Takis Konstantopoulos & Thomas Mountford, 2018. "Power Law Condition for Stability of Poisson Hail," Journal of Theoretical Probability, Springer, vol. 31(2), pages 684-704, June.

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