Orateur
Aziz Ben Nejma
Description
In 2024, Chewi and Stromme showed that, in the low-temperature regime, the behavior of the relative entropy with respect to a Gibbs measure reflects that of the underlying potential when the latter has a unique minimizer. They conjectured that this link extends more generally to potentials having multiple minimizers.
In this talk, we show that this is not the case. We explain that when there are multiple minimizers, the geometry of the set of minimizers plays a direct role in how the constants in functional inequalities behave at low temperature.