Necessary and Sufficient Conditions for the GHS Inequality with Applications to Analysis and Probability

DOI10.2307/1997611zbMath0412.35084OpenAlexW4235930103MaRDI QIDQ4200611

Richard S. Ellis, Charles M. Newman

Publication date: 1978

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1997611

zbMATH Keywords

probabilitydiffusion processesanalysisequilibrium statistical mechanicsIsing model of ferromagnetismconvexity-preserving propertiesGriffiths-Hurst-Sherman inequality

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Electromagnetic theory (general) (78A25) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (13)

Large deviations and the maximum entropy principle for marked point random fields ⋮ Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions ⋮ Interface in a one-dimensional Ising spin system ⋮ Hölder continuity of sample paths in Euclidean field theory ⋮ Limit theorems for sums of dependent random variables occurring in statistical mechanics ⋮ Expansions of the maximum principle: Exponential preservation by the heat equation ⋮ PDE/statistical mechanics duality: relation between Guerra's interpolated \(p\)-spin ferromagnets and the Burgers hierarchy ⋮ Diffusion equation techniques in stochastic monotonicity and positive correlations ⋮ Limit theorems for sums of dependent random variables occurring in statistical mechanics ⋮ Small random perturbation of a classical mean field model ⋮ The GHS inequality and the Riemann hypothesis ⋮ Entropy production by block variable summation and central limit theorems ⋮ Symmetry breaking and random waves for magnetic systems on a circle

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