6 problems

Inverse-square variance conjecture.

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

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

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 $R^{(0)}_{n,k}$ 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 $k\geq0$,