5 problems

Let $\Delta_k$ denote the optimal asymptotic MSE constant within the generalized grouping (GG) family for groups of size $k$. Monotonicity conjecture. … i.e., the optimal asymptoti…

Let $X$ be a radial Riemannian manifold with stationary probability distribution $p(x)\propto{\mathrm{e}^{-V(x)}}$. Suppose an update scheme changes the radial component in a non-t…

Pivot time-scale conjecture. The integrated autocorrelation time of this observable is of the same order as the time required to make successful pivots at all length scales with re…

Let $T\in(0,\infty)$, let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space with a normal filtration $(\mathcal{F}_t)_{t\in[0,T]}$, let $W^{l,k}$ be a family of independent…

Let $\left(\overline{\mathcal R_{[L]}}\right)_{L=1,2,\dots}$ be a sequence of restriction operators whose macroscopic state variables are the first $L$ centralized moments, with…