Critical behavior and the limit distribution for long-range oriented percolation. I

DOI10.1007/s00440-007-0101-2zbMath1149.60065arXivmath/0703455OpenAlexW2110927606MaRDI QIDQ948938

Lung-Chi Chen, Akira Sakai

Publication date: 16 October 2008

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

Full work available at URL: https://arxiv.org/abs/math/0703455

Mathematics Subject Classification ID

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

Related Items

Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation ⋮ 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 ⋮ Long-range self-avoiding walk converges to \(\alpha\)-stable processes ⋮ Asymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolation ⋮ Critical exponents for long-range \(\mathrm O(n)\) models below the upper critical dimension ⋮ Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk ⋮ Critical two-point function for long-range models with power-law couplings: the marginal case for \({d\ge d_{\mathrm{c}}}\) ⋮ Hyperscaling for oriented percolation in \(1+1\) space-time dimensions ⋮ High-dimensional incipient infinite clusters revisited ⋮ Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees ⋮ Critical two-point functions for long-range statistical-mechanical models in high dimensions

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