7 problems

Optimal sampling-rate conjecture. One may conjecture that

Nonexistence conjecture. The condition derived in the paper for the nonexistence of a Gerow–Robson density on $M(n)$ holds for every $n\geq 6$.

Let $p_1,p_2,\dots$ be a sequence of arbitrary discrete distributions presented adaptively over time. An online random sampling algorithm generates exact samples from these distrib…

Let $d\geq 1$ and let $\varepsilon>0$. Consider online random sampling algorithms that, for every sequence of distributions on a $d$-element alphabet, generate independent samples…

Let $\mathrm{SG}$ be the Sierpiński gasket, let $\mathcal{L}$ be its Laplacian, and let $\mathcal{L}_\epsilon(\omega)$ be the random graph averaging Laplacian defined from random s…

Stability conjecture. Eigenmaps of the random averaging Laplacians give numerically stable locally uniform approximations to the corresponding eigenmap of $\mathcal{L}_{(g)}$. This…

Let $G$ be a graph with $n$ vertices and maximum degree $\Delta$. Consider the Markov chain whose states are the proper $(\Delta+2)$-colorings of $G$, with transitions given by loc…