9 problems

Maximum–record equivalence conjecture. The asymptotic relation

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…

Let $R_{n,k}$ count records through time $n$ that break precisely $k$ remaining records, and write … For fixed $k\geq0$, sharper variance asymptotics conjecture. There exist consta…

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

Observations-time strong law 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

Let $K_n$ be the number of remaining records broken at the $n$th record, let $C_k$ denote the coefficient appearing in the approximation to $\operatorname{\mathbb P{}}(K_n=k)$, let…