Construction of the Incipient Infinite cluster for spread-out oriented percolation above \(4 + 1\) dimensions

DOI10.1007/s00220-002-0728-xzbMath1013.82017OpenAlexW2168267254MaRDI QIDQ1865605

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

Publication date: 27 March 2003

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-002-0728-x

zbMATH Keywords

super-Brownian motionincipient infinite cluster measurespread-out oriented percolation

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Time-dependent percolation in statistical mechanics (82C43)

Related Items (13)

Multi-arm incipient infinite clusters in 2D: scaling limits and winding numbers ⋮ Infinite canonical super-Brownian motion and scaling limits ⋮ The survival probability and \(r\)-point functions in high dimensions ⋮ The survival probability for critical spread-out oriented percolation above \(4 + 1\) dimensions. I. Induction. ⋮ Random graph asymptotics on high-dimensional tori ⋮ 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 ⋮ Random walk on the high-dimensional IIC ⋮ Invasion percolation on regular trees ⋮ Mean-field driven first-order phase transitions in systems with long-range interactions ⋮ High-dimensional incipient infinite clusters revisited ⋮ The Alexander-Orbach conjecture holds in high dimensions

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