9 problems

Arnold's density-profile conjecture. Asymptotically for large ${\bf d}^m$, the density at $s$ is

Arnold's average-density conjecture. For large ${\bf d}^m$, with overwhelming probability, this fraction is asymptotically $1/m$; equivalently,

Asymptotic linear-form conjecture. Under the setting of Theorem InfluenceQuantiles-main,

The averaged Zaremba conjecture. For $N\in\mathbb{N}$,

Let $\overline{H}$ be the matrix appearing in the maxT procedure, let $\iota$ denote the all-ones vector, and define … Suppose that $E$ has independent and identically distributed…

Let the sample $\mathbf{y}$ consist of elements that can be uniquely ordered, and let the quantile $q\in(0,1)$ be fixed. Let $\psi$ denote the index of the original order statistic…

Let $f_0$ be the monotone regression function, let $x_0$ be the point of inference, and let $\widehat{f}_n^{-}(x_0)$ be the block max-min estimator with associated block count…

Let $F_0$ and $H$ be continuously differentiable at $t_0$ and $(t_0,t_0)$, respectively, with strictly positive derivatives $f_0(t_0)$ and $h(t_0,t_0)$, where $H$ is the distributi…

Let $(\varepsilon_n)$ be a martingale difference sequence satisfying the homogeneity condition … and assumption $(H_p)$ introduced in the preceding theorem, for some integer…