Stability for the logarithmic Sobolev inequality

Mathphys Analysis Seminar

The logarithmic Sobolev inequality compares the relative (with respect to the standard Gaussian) entropy of a density with its relative Fisher information. Having the sharp constant and the optimal functions been established, the question of stability is posed. In this talk, new constructive stability results due to Jean Dolbeault, Nikita Simonov, and the speaker are discussed. Our technique relies on refined properties of the heat flow, in particular the carrè du champ method.