The Gibbs measures and partial differential equations. I. Ideas and local aspects

DOI10.1007/BF01220997zbMath0608.60093MaRDI QIDQ1085903

Bogusław Zegarliński

Publication date: 1986

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

zbMATH Keywords

Dirichlet problemsGibbs measuresEuclidean field theoryEuclidean field with interaction

Mathematics Subject Classification ID

Random fields (60G60) Boundary value problems for second-order elliptic equations (35J25) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Constructive quantum field theory (81T08)

Related Items

On the DLR equation for the \((\lambda:\phi^ 4: +b:\phi^ 2:+\mu\phi\), \(\mu\neq 0)_ 2\) Euclidean quantum field theory: The uniqueness theorem, Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions, Uniqueness of Gibbs states for general \(P(\phi)_ 2\)-weak coupling models by cluster expansion

Cites Work

• Remarks on McBryan's convergence proof for \((\alpha ^{-4}(\cos (\alpha \phi)-1+\alpha ^ 2\phi ^ 2/2))_ 2\)-quantum fields
• Uniqueness and the global Markov property for Euclidean fields: The case of general exponential interaction
• Remarks on the global Markov property
• Uniqueness and the global Markov property for Euclidean fields. The case of trigonometric interactions
• Euclidean nonlinear classical field equations with unique vacuum
• Specifications and Martin boundaries for \(\mathcal P(\phi)_2\)-random fields
• The D.L.R. conditions for translation invariant Gaussian measures on L(R d)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item