14 problems

For the birth Mallows process, let $J_t=|\{k\leq\binom{n}{2}:T_k\leq t\}|$ be the number of jumps by time $t$. Gaussian Markov-limit conjecture. As $n$ tends to infinity, … where…

Let $f$ be a smooth stationary Gaussian process, let $K(r)$ denote its correlation function, and let the Poisson approximation refer to the approximation for the locations and size…

Cosine covariance conjecture. For every $n\geq 1$, every correlation matrix $\Sigma$, and every $t\geq 0$,

Stochastic codimension conjecture. For every Borel set $F$ in the state space,

Equispaced Fourier Matérn matrix error bound. With high probability as $N\to\infty$,

Let $H>1/2$, and consider fractional Gaussian noise with Hurst parameter $H$. For any element of this process, project it onto any finite number of its subsequent elements, and den…

Weak variance conjecture. The expected spectral norm satisfies

Let $p\geq 1$, let $n,m$ be positive integers, let $(a_{ijk})_{i,j\leq n,k\leq m}$ be a triple-indexed real matrix, let $T\subset\mathbb R^m$ be bounded and nonempty, and let $g_i$…

Let $X=(X_{ij})_{1\leq i,j\leq n}$ be the centered Gaussian random matrix considered in this section, with entry standard deviations $b_{ij}$, and assume without loss of generality…

Let $X$ be the $d\times d$ symmetric random matrix with entries $X_{ij}=b_{ij}g_{ij}$, where $\{g_{ij}:i\ge j\}$ are independent standard Gaussian random variables and…

Zero-set absolute-continuity conjecture. For every $t\geq 0$, the Slepian zero set on $[0,t]$ is mutually absolutely continuous with respect to the zero set of Brownian motion star…

Convergence-rate conjecture.

Let $Z$ be a spatial process with spectral density $f$ satisfying condition (f-cond), let $N_\varepsilon$ be a set of observations approaching the origin, and let $b(r)$ denote the…

Gaussian consistency conjecture. If $X$ is a Gaussian stationary process with $\|RX\|_1<\infty$, then $S_J[\mathcal P_J]X$ is a mean-square consistent estimator of $\overline S X$.…