12 problems

Let $f_t$ be a solution of the Boltzmann equation, and let its Fisher information be denoted by $I(f_t)$. McKean's conjecture. The Fisher information $I(f_t)$ is monotonically decr…

Entropic-gap conjecture. With a bit more work, there is a constant $K>0$ such that

Gaussian completely monotone conjecture. For all $m\geq1$ and all $t>0$,

Let $\rho_0\in\mathcal{P}_V$, let $S_r$ be the stated class of flows, and for $u\in S_r$ define the pushforward measure $\rho_t=u(t,\cdot)_{\#}\rho_0$. For $u$-regularized Stein F…

Let $({\mathcal P}_{\mathcal X},{\mathcal D}_{\mathcal X})$ be a 2-integrable weakly $C^k$-diffeological statistical model, let $\varphi$ be a $V$-valued function on…

Fisher-information conjecture. The bound above also holds for the Fisher information of $U_k$ itself, rather than only for the increment processes $\bar U_k$.

Rate-optimality conjecture. Due to the singularity of the Fisher matrix, the achieved rates $$ are in fact optimal.

Let $\mathcal{S}_N$ be the symmetric subspace of $N$ qubits, let $\mu(\mathcal{S}_N)$ denote its unitarily invariant probability measure, and let…

Prokopenko et al.'s conjecture. It is enough to consider the entries of the Fisher information matrix rather than order parameters.

Uniform lower-bound conjecture. For any fixed rank $r$, $lambda_{min}$ is larger than a fixed constant for all states of rank $r$, regardless of the number of ions.

Alternating-sign conjecture. The signs of all subsequent derivatives of $H(X+Z_t)$ alternate, extending the explicitly verified alternating-sign property through order four.

Fisher information equality conjecture. The Fisher information with respect to $\alpha$ is identical for the two probability-distribution families