9 problems

Chewi–Stromme conjecture.

Let $\mu\in\mathcal{P}(\mathbb{R}^d)$ be an isotropic distribution, meaning that … Let $\nu_n$ denote the normalized $n$-fold convolution sequence from the central limit theorem, s…

Salez–Youssef conjecture. There is a universal constant $c>0$ such that

Ollivier-Ricci curvature and LSI. There exists a universal constant $c<\infty$ such that whenever the Ollivier-Ricci curvature $\tilde{\kappa}$ is positive, we have

Log-Sobolev constant limit conjecture. Under assumptions A1 and A2,

Let $\kappa=(\kappa_1,\ldots,\kappa_L)$ be the parameter defining the multislice, let $\tau_{\textsc{ls}}(\kappa)$ denote the log-Sobolev constant of its transposition walk, and se…

Consider an inhomogeneous zero-range process with $n$ sites, rate functions $r_i$, particle number $m$, and site weights $p=(1/n,\ldots,1/n)$. Assume that there are constants…

Peres–Tetali conjecture. The modified log-Sobolev constant satisfies

Zero-potential Log-Sobolev conjecture. For $Q\equiv0$, $LSI(1/2)$ is true. The paper proves that $LSI((1+\delta)/4)$ holds for some $\delta>0$, and conjectures the stronger coeffic…