Tags » Log-Sobolev Inequality

Follmer's drift, Ito's lemma, and the log-Sobolev inequality

1. Construction of Föllmer’s drift

In a previous post, we saw how an entropy-optimal drift process could be used to prove the Brascamp-Lieb inequalities. Our main tool was a result of Föllmer that we now recall and justify. 1,061 more words


285G, Lecture 8: Ricci flow as a gradient flow, log-Sobolev inequalities, and Perelman entropy

It is well known that the heat equation


on a compact Riemannian manifold (M,g) (with metric g static, i.e. independent of time), where is a scalar field, can be interpreted as the… 4,259 more words