Expansion in High Dimension for the Growth Constants of Lattice Trees and Lattice Animals

DOI10.1017/S0963548313000102zbMath1346.60140arXiv1208.3513OpenAlexW2164689216MaRDI QIDQ2841489

Gordon Slade, Yuri Mejia Miranda

Publication date: 26 July 2013

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3513

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41)

Related Items (4)

Self‐avoiding walk on the hypercube ⋮ Unnamed Item ⋮ The growth rate of high-dimensional tree polycubes ⋮ NoBLE for lattice trees and lattice animals

Cites Work

• Unnamed Item
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• The growth constants of lattice trees and lattice animals in high dimensions
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• The scaling limit of lattice trees in high dimensions
• Mean-field lattice trees
• A pattern theorem for lattice clusters
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• Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions
• On the upper critical dimension of lattice trees and lattice animals
• 1/d-expansions for the free energy of weakly embedded site animal models of branched polymers
• Expansion in ${\boldsymbol{n^{-1}}}$ for Percolation Critical Values on the $n$-cube and ${\boldsymbol{{\mathbb Z}^n}}$: the First Three Terms
• Borel-type bounds for the self-avoiding walk connective constant
• 1/d-expansions for the free energy of lattice animal models of a self-interacting branched polymer
• Lattice trees and super-Brownian motion
• The Self-Avoiding-Walk and Percolation Critical Points in High Dimensions
• Relationships between growth constants for animals and trees (lattice theory)
• Self-avoiding walk enumeration via the lace expansion
• Cell Growth Problems
• Asymptotic expansions inn−1 for percolation critical values on then-Cube and ℤn

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