4 problems

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 $k\geq0$,

For each $M\geq1$ and $k\geq0$, let $\tilde p_{M,k}$ be the fraction of the first $M$ records that break precisely $k$ remaining records. Strong law conjecture. For every fixed…

Glivenko–Cantelli conjecture. The empirical fractions satisfy