Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/104270
Title: The Continuity of M and N in Greedy Lattice Animals
Authors: Lee, S. 
Keywords: Lattice animals
Self-avoiding paths
Issue Date: 1997
Source: Lee, S. (1997). The Continuity of M and N in Greedy Lattice Animals. Journal of Theoretical Probability 10 (1) : 87-100. ScholarBank@NUS Repository.
Abstract: Let {Xv: v ∈ Zd}, d ≥ 2, be i.i.d. positive random variables with the common distribution F which satisfy, for some a > 0, ∫ xd(log+ x)d+a dF(x) < ∞. Define Mn = max {Σv∈π Xv: π a selfavoiding path of length n starting at the origin} Nn = max {Σv∈ξ Xv : ξ a lattice animal of size n containing the origin} Then it has been shown that there exist positive finite constants M = M[F] and N = N[F] such that M N limn → ∞ Mn/n and limn → ∞ Nn/n = N a.s. and in L1.
Source Title: Journal of Theoretical Probability
URI: http://scholarbank.nus.edu.sg/handle/10635/104270
ISSN: 08949840
Appears in Collections:Staff Publications

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