The Self-Avoiding-Walk and Percolation Critical Points in High Dimensions

DOI10.1017/S0963548300001607zbMath0838.60087OpenAlexW2020435017MaRDI QIDQ4862743

Takashi Hara, Gordon Slade

Publication date: 17 March 1996

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

Full work available at URL: https://doi.org/10.1017/s0963548300001607

zbMATH Keywords

percolationself-avoiding walksBernoulli bond percolationexistence of an asymptotic expansion in the inverse dimension

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Statistical mechanics of polymers (82D60) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

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Critical two-point functions and the lace expansion for spread-out high-dimensional percolation and related models., Expansion for the critical point of site percolation: the first three terms, Self-avoiding walks and trees in spread-out lattices, Critical site percolation in high dimension, Percolation on nonunimodular transitive graphs, Self‐avoiding walk on the hypercube, Mean-field behavior of nearest-neighbor oriented percolation on the BCC lattice above \(8 + 1\) dimensions, Anisotropic non-oriented bond percolation in high dimensions, Conformally invariant scaling limits in planar critical percolation, Series expansion of the percolation threshold on hypercubic lattices, The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion, Existence of a non-averaging regime for the self-avoiding walk on a high-dimensional infinite percolation cluster, Formulae and growth rates of high-dimensional polycubes, New lower bounds on the self-avoiding-walk connective constant, Polygons and the Lace Expansion, Expansion in High Dimension for the Growth Constants of Lattice Trees and Lattice Animals, Entanglement percolation and spheres in \(\mathbb{Z}^d\), Random subgraphs of finite graphs. II: The lace expansion and the triangle condition, Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions

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