The log-Sobolev inequality with quadratic interactions
  We assume one site measures without a boundary $e^{-\phi(x)}dx/Z$ 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. 
Ioannis Papageorgiou (UBA, Conicet)
math.FA math-ph math.MP math.PR