Gaussian limit for critical oriented percolation in high dimensions.

DOI10.1007/BF02183691zbMath1114.82304OpenAlexW1970232328MaRDI QIDQ1593185

Bao Gia Nguyen, Wei-Shih Yang

Publication date: 16 January 2001

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02183691

zbMATH Keywords

critical exponentconnectivity functionlace expansioninfrared boundmean-field behaviorOriented percolationGaussian limitparallel correlation length

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items (14)

Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation ⋮ Infinite canonical super-Brownian motion and scaling limits ⋮ The survival probability and \(r\)-point functions in high dimensions ⋮ Mean-field behavior of nearest-neighbor oriented percolation on the BCC lattice above \(8 + 1\) dimensions ⋮ Asymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolation ⋮ An expansion for self-interacting random walks ⋮ The scaling limit of loop-erased random walk in three dimensions ⋮ The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion ⋮ Critical behavior and the limit distribution for long-range oriented percolation. I ⋮ Hyperscaling for oriented percolation in \(1+1\) space-time dimensions ⋮ \(R\)-positivity, quasi-stationary distributions and ratio limit theorems for a class of probabilistic automata ⋮ NoBLE for lattice trees and lattice animals ⋮ Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees ⋮ Loop-erased random walk on a torus in dimensions 4 and above

Cites Work

• Gaussian fluctuations of connectivities in the subcritical regime of percolation
• Mean-field critical behaviour for percolation in high dimensions
• Tree graph inequalities and critical behavior in percolation models
• The diffusion of self-avoiding random walk in high dimensions
• The scaling limit of self-avoiding random walk in high dimensions
• Percolation critical exponents under the triangle condition
• Self-avoiding walk in five or more dimensions. I: The critical behaviour
• The number and size of branched polymers in high dimensions
• Triangle condition for oriented percolation in high dimensions
• Sharpness of the phase transition in percolation models
• Mean-field critical behaviour for correlation length for percolation in high dimensions
• The critical contact process dies out
• On the upper critical dimension of lattice trees and lattice animals
• Some general results concerning the critical exponents of percolation processes
• THE LACE EXPANSION FOR SELF-AVOIDING WALK IN FIVE OR MORE DIMENSIONS
• Oriented percolation in dimensions d ≥ 4: bounds and asymptotic formulas

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