4 problems

Log-Sobolev KLS conjecture.

Let $\mu$ be a log-concave probability measure on $\mathbb R^n$. It is $\beta$-tilt-stable if, for every $h\in\mathbb R^n$, the covariance operator of the tilted measure…

Let $\rho_t$ denote the solution of the Langevin Fokker–Planck equation with initial density $\rho_0$, and let the target density $\pi$ satisfy the log-Sobolev inequality (LSI). As…

Ferromagnetic comparison conjecture. The measure $\mu_{\Lambda}$ satisfies a log-Sobolev inequality with constant $\varrho$ such that