The log-Sobolev inequality with quadratic interactions

Abstract

We assume one site measures without a boundary $e^{-\varphi (x)}dx/Z$ that satisfy a log-Sobolev inequality. We prove that if these measures are perturbed with quadratic interactions, then the associated infinite dimensional Gibbs measure on the lattice always satisfies a log-Sobolev inequality. Furthermore, we present examples of measures that satisfy the inequality with a phase that goes beyond convexity at infinity.

42 pages

References in corpus (5)

• Logarithmic Sobolev inequalities for infinite dimensional Hörmander type generators on the Heisenberg group
• Functional inequalities and uniqueness of the Gibbs measure -- from log-Sobolev to Poincaré
• The Logarithmic Sobolev Inequality in Infinite dimensions for Unbounded Spin Systems on the Lattice with non Quadratic Interactions
• A note on the Modified Log-Sobolev inequality
• The Logarithmic Sobolev Inequality for Gibbs measures on infinite product of Heisenberg groups

Cited by in corpus (1)

• The log-Sobolev inequality for spin systems of higher order interactions