Mean-field behavior of nearest-neighbor oriented percolation on the BCC lattice above \(8 + 1\) dimensions

DOI10.1007/s11040-022-09441-6OpenAlexW4320733771MaRDI QIDQ2685531

Satoshi Handa, Yoshinori Kamijima, Lung-Chi Chen

Publication date: 22 February 2023

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.14211

zbMATH Keywords

lace expansionnearest-neighbor modeloriented percolationmean-field behaviorupper critical dimension

Mathematics Subject Classification ID

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

Cites Work

• A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model
• Hyperscaling for oriented percolation in \(1+1\) space-time dimensions
• Mean-field critical behaviour for percolation in high dimensions
• Critical behavior and the limit distribution for long-range oriented percolation. I
• Self-avoiding walk in 5 or more dimensions
• Tree graph inequalities and critical behavior in percolation models
• Percolation critical exponents under the triangle condition
• Triangle condition for oriented percolation in high dimensions
• Gaussian limit for critical oriented percolation in high dimensions.
• A generalised inductive approach to the lace expansion
• The box-crossing property for critical two-dimensional oriented percolation
• Generalized approach to the non-backtracking lace expansion
• Sharpness of the phase transition in percolation models
• Convergence of critical oriented percolation to super-Brownian motion above \(4+1\) dimensions
• Progress in high-dimensional percolation and random graphs
• A survey on the lace expansion for the nearest-neighbor models on the BCC lattice
• The lace expansion and its application. École d'Été de Probabilités de Saint-Flour XXXIV -- 2004.
• 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
• Mean-field behavior for nearest-neighbor percolation in \(d>10\)
• The critical contact process dies out
• Universality classes in nonequilibrium lattice systems
• Expansion in ${\boldsymbol{n^{-1}}}$ for Percolation Critical Values on the $n$-cube and ${\boldsymbol{{\mathbb Z}^n}}$: the First Three Terms
• Inequalities with applications to percolation and reliability
• On the critical percolation probabilities
• Percolation
• The Self-Avoiding-Walk and Percolation Critical Points in High Dimensions
• Asymptotic expansions inn−1 for percolation critical values on then-Cube and ℤn
• Expansion for the critical point of site percolation: the first three terms
• Mean-field critical behavior for the contact process
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Mean-field behavior of nearest-neighbor oriented percolation on the BCC lattice above \(8 + 1\) dimensions