10 problems

Inverse-square variance conjecture.

Bounded-variance conjecture. As $v$ tends to infinity,

Davies et al.'s variance conjecture. For any $\lambda>0$,

$M^{-1}$ variance conjecture. If $\nu$ is dominated by $\lambda_\mathbb{X}$, then this variance attains the order of

$M^{-1}$ variance conjecture. If $\xi\sim\nu$, the variance could potentially attain the order of

Let $\mathcal M_{\kappa}$ be the set of positive-definite $n\times n$ matrices with condition number $\kappa$. For $k<n$, $\kappa$, and $M\in\mathcal M_{\kappa}$, define $Y_k(M)$ a…

Let $R^{(1)}_{n,k}$ count, through time $n$, records that break precisely $k$ remaining records and set a record in the first coordinate but not the second, and let…

Let $R^{(0)}_{n,k}$ count, through time $n$, records that break precisely $k$ remaining records and do not set a record in either coordinate. Reduced variance bound conjecture. For…

Variance bound conjecture. For each fixed $k\geq0$,

Let $L_n$ denote the perimeter of the convex hull of the first $n$ steps of a planar random walk, and suppose the degenerate case holds in which … with probability $1$, so that the…