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- W2033871111 abstract "Let ${X_nu: nu in mathbb{Z}^d}$ be an i.i.d. family of positive random variables. For each set $xi$ of vertices of $mathbb{Z}^d$, its weight is defined as $S(xi) = sum_{nu in xi}X_nu$. A greedy lattice animal of size $n$ is a connected subset of $mathbb{Z}^d$ of $n$ vertices, containing the origin, and whose weight is maximal among all such sets. Let $N_n$ denote this maximal weight. We show that if the expectation of $X^d_nu(log^+ X_nu)^{d+ a}$ is finite for some $a > 0$, then w.p.1 $N_n leq Mn$ eventually for some finite constant $M$. Estimates for the tail of the distribution of $N_n$ are also derived." @default.
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- W2033871111 date "1993-11-01" @default.
- W2033871111 modified "2023-09-30" @default.
- W2033871111 title "Greedy Lattice Animals I: Upper Bounds" @default.
- W2033871111 doi "https://doi.org/10.1214/aoap/1177005277" @default.
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