The survival probability for critical spread-out oriented percolation above \(4 + 1\) dimensions. I. Induction.

DOI10.1007/s00440-006-0028-zzbMath1130.60094OpenAlexW3113614475MaRDI QIDQ880936

Gordon Slade, Remco van der Hofstad, W. Th. F. den Hollander

Publication date: 21 May 2007

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-006-0028-z

zbMATH Keywords

survival probabilityspread-out oriented bond percolation

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (7)

Infinite canonical super-Brownian motion and scaling limits ⋮ The survival probability and \(r\)-point functions in high dimensions ⋮ On the range of lattice models in high dimensions ⋮ Electrical resistance of the low dimensional critical branching random walk ⋮ Random walk on the incipient infinite cluster for oriented percolation in high dimensions ⋮ Arm exponents in high dimensional percolation ⋮ Weak convergence of measure-valued processes and \(r\)-point functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension: the higher-point functions
• Random walk on the incipient infinite cluster for oriented percolation in high dimensions
• Percolation critical exponents under the triangle condition
• Triangle condition for oriented percolation in high dimensions
• An application of the voter model: Super-Brownian motion invariance principle.
• A generalised inductive approach to the lace expansion
• Gaussian scaling for the critical spread-out contact process above the upper critical dimension
• Sharpness of the phase transition in percolation models
• Construction of the Incipient Infinite cluster for spread-out oriented percolation above \(4 + 1\) dimensions
• Convergence of critical oriented percolation to super-Brownian motion above \(4+1\) dimensions
• The survival probability for critical spread-out oriented percolation above \(4+1\) dimensions. II: Expansion
• Weak convergence of measure-valued processes and \(r\)-point functions
• Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions
• The critical contact process dies out
• The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion
• Asymptotics for interacting particle systems onZ d
• Mean-field critical behavior for the contact process

This page was built for publication: The survival probability for critical spread-out oriented percolation above \(4 + 1\) dimensions. I. Induction.