Hypercontractivity for spin systems of infinite extension

DOI10.1007/BF01192197zbMath0820.60082MaRDI QIDQ1346966

Étienne Laroche

Publication date: 23 April 1995

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

zbMATH Keywords

spectral gapmixing conditionspin systemSobolev constantinfinite range Gibbs potential

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)

Related Items (9)

Invariance implies Gibbsian: some new results ⋮ Exponential inequalities and functional central limit theorems for random fields ⋮ Equivalence of a mixing condition and the LSI in spin systems with infinite range interaction ⋮ An SMB approach for pressure representation in amenable virtually orderable groups ⋮ Glauber dynamics for fermion point processes ⋮ Coupling, concentration inequalities, and stochastic dynamics ⋮ Coercive inequalities for Gibbs measures ⋮ Relaxed criteria of the Dobrushin-Shlosman mixing condition ⋮ On the ergodic properties of Glauber dynamics.

Cites Work

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• Log-Sobolev inequalities for infinite one-dimensional lattice systems
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• The stochastic Heisenberg model
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• The equivalence of the logarithmic Sobolev inequality and the Dobrushin- Shlosman mixing condition
• The logarithmic Sobolev inequality for discrete spin systems on a lattice
• Gibbs measures and phase transitions
• Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics
• For 2-D lattice spin systems weak mixing implies strong mixing
• Logarithmic Sobolev inequalities and stochastic Ising models
• Completely analytical interactions: Constructive description
• On log-Sobolev inequalities for infinite lattice systems
• Inégalités de Sobolev et minorations du semi-groupe de la chaleur

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