The log-Sobolev inequality with quadratic interactions
We assume one-site measures without a boundary e−ϕ(x)dx/Z that satisfies 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,...
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00222488_v59_n8_p_Papageorgiou |
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| Sumario: | We assume one-site measures without a boundary e−ϕ(x)dx/Z that satisfies 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. © 2018 Author(s). |
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