9 problems

Low-degree conjecture. If there exist $\epsilon>0$ and $D=D(n)\geq (\log n)^{1+\epsilon}$ such that

Detection threshold conjecture. The largest dimension at which the random geometric graph can be statistically distinguished from the Erdős–Rényi graph with the same edge density s…

Low-degree conjecture. For suitably “nice” detection tasks, low-degree polynomials should match the power of all polynomial-time algorithms.

Spectral detection conjecture. The sharp threshold for distinguishing the RGG from its Erdős–Rényi counterpart is determined by

Bubeck et al.'s geometry-loss conjecture. The geometry of a sparse RGG is lost once

Let ${\mathcal X}={\mathcal Y}={\mathbb R}$, let ${\mathsf P}_{X,Y}$ be a fixed distribution independent of $n$, and define the likelihood ratio … Let ${\mathcal L}$ be the likelih…

Let $K$ be even, let $\mu_1=\mu_3=\ldots=\mu_{K+1}=0$, and consider a signal with well-spaced non-null segments. A change point is $(\kappa,q)$-high energy when it satisfies the co…

Consider the $d$-dimensional integer lattice with $d\ge 3$, viewed as a torus, and let $\mathcal{C}$ be the class of self-avoiding paths of length $k\le m$ starting at a known loca…

Let $\Theta_1(k_n,\zeta_n)$ be the parameter space of vectors $\theta\in\mathbb{R}^n$ with at most $k_n=n^\beta$ nonzero coordinates and satisfying…