26 problems

Conjecture on failure for $p>2$. For some closed Riemannian manifolds and some $p>2$, this inequality fails.

Let $\mathbb{Z}_n=\{0,1,\dots,n-1\}$ be the finite cyclic group with normalized counting measure, and let $(P_t)_{t\in\mathbb{R}_+}$ be the Poisson-like semigroup defined by … wher…

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

Uniform LSI conjecture. Under suitable additional assumptions, uniqueness of the stationary solution of the mean-field limit, equivalently uniqueness of the solution of the associa…

The discussion concerns convolution kernels subject to polynomial weights of the form $(1+|x|^\beta)f(x)$, with parameters $\beta\in[0,\infty)$ and $r\in[1,\infty)$. Kernel-failure…

Consider the log-Sobolev inequalities associated with the multimode phase-covariant Gaussian channels, and let the corresponding multimode log-Sobolev constants be compared with th…

Let the quantum Ornstein–Uhlenbeck semigroup be considered on quantum states, and let the 1-log-Sobolev inequality mean the modified log-Sobolev inequality for this semigroup. Gaus…

Pedrotti's conjecture. Positive Ollivier curvature, together with non-negative $\ell_\infty$ Wasserstein curvature, implies a modified log-Sobolev inequality.

Tetali–Peres conjecture. Lower Ollivier curvature bounds imply modified log-Sobolev inequalities.

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

Limiting log-Sobolev constant conjecture. Under assumptions A1 and A2, the limit of the particle-system log-Sobolev constants is uniquely characterised by the mean-field dissipatio…

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…

Log-Sobolev averaging conjecture. These assumptions should be sufficient to establish convergence of the non-commutative law in the large $k$ limit and the external averaging prope…

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…

Quantum Log-Sobolev regularity conjecture. Every detailed balanced Lindbladian satisfies $L_p$-regularity, and every primitive Lindbladian satisfies a weak version of it.

Let $({\mathcal{X}},T_t,\pi)$ be a Markov semigroup and let its tensorization be denoted by $T_t^{\otimes n}$. Fix $p_0>1$ and $0<\rho_0<(1-p_0^{-1})\ln 2$, and define … Also defin…

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

Peres–Tetali conjecture. A modified log-Sobolev inequality should always hold in this setting.

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…

Optimal free Log-Sobolev inequality conjecture. The inequality $LSI(\rho)$ should hold, meaning

Non-Lipschitz moment conjecture. There is a constant $C_D$ such that

Let $c(\delta)$ be the optimal log-Sobolev constant, and consider the upper bounds in Theorems 1 and 2 for measures whose supports have a prescribed radius. Uniform sharpness conje…