8 problems

Let $\mu$ be a probability measure on $\{0,1\}^{\mathbb{N}}$, let $X\sim\mu$, and let $\Delta_n(\mu)$ be the expected uniform absolute deviation of the associated centered, normali…

Let $\mu$ be a probability measure on $\{0,1\}^{\mathbb{N}}$, let $X\sim\mu$, and let $\Delta_n(\mu)$ denote the expected supremum norm of the centered empirical mean. Pairwise-cor…

Under Assumption … sigma^Y{i,j}geq sigma^X{i,j}geq 0 … operatorname{Cov}(log SN({mathbf G}),pi({mathbf G})pj({mathbf G}))leq 0. … ; its resolution is not indicated in the supplied…

Let $\Lambda(n)$ denote the von Mangoldt function and let $\mu(n)$ denote the Möbius function. For $X\to\infty$, let $H=X^\delta$ with $\delta\in(0,1)$ and average over…

Let $\bX_1,\dots,\bX_n$ be jointly distributed $\{\pm1\}$-valued random variables. Conditioning on a random subset of $O(1/\eps^2)$ variables is known to reduce their average pairw…

Covariance-decay conjecture. Under these assumptions, one should have

Let $G=(V,A)$ be a directed acyclic graph, and let $\Sigma$ denote the covariance matrix of its arc-indicator variables. Covariance-matrix sparsity conjecture. The covariance matri…

Let $G=(V,A)$ be a directed acyclic graph, with arcs represented by indicator random variables $A_{ij}$ and covariance matrix $\Sigma$. Two arcs are incident when they share a comm…