| Contents |
| In this talk we discuss the quasi-tensorization of the relative entropy for Gibbs measures. By transferring Katalyn Marton's argument from continuous to discrete state-spaces, we derive a criterion for the quasi-tensorization in discrete state-spaces. The criterion seems to be the first one of its kind and is optimal for product measures. The criterion can be interpreted as a generalization of the Otto-Reznikoff criterion for the logarithmic Sobolev inequality (LSI) to discrete state spaces. Applying the criterion to the Curie-Weiss and Ising modell, one can deduce uniform estimates on the modified LSI for the Gibbs sampler in the regime of small interaction. |
|