7 problems

Let $(\vartheta,\tau,\sigma)$ be parameter values, and let $H^{(\vartheta,\tau,\sigma)}$ be the limit distribution of the empirical distribution functions of the interspike times,…

Let $D_{\mathcal{C},\frac{d+1}{2}}$ denote the discrepancy sum at the critical index, for a strictly convex body $\mathcal{C}$ in the setting considered in the paper. Cauchy limit…

Let $F_Q$ be the set of all reduced fractions in $[0,1]$ with denominator at most $Q$. For a reduced fraction $p/q\in F_Q$, let $L(p/q,q)$ be the unsymmetrized lattice and let…

Let $L(\alpha,N)$ be the unsymmetrized lattice associated with $\alpha\in[0,1]$ and $N$, and let $D_2$ denote its $L^2$ discrepancy. Suppose that $\alpha$ is chosen randomly from…

Let $t$ tend to infinity along the real axis, and consider the function-valued random elements obtained from the vertical translates $u\mapsto \zeta(\tfrac12+i(t+u))$, with values…

Let $f$ be the monotone function and let $\widehat f_n$ be the Grenander-type estimator considered in the paper. Let $\widetilde f_n$ denote either the modified estimator in Kuliko…

Gaussian perimeter limit-law conjecture. The mean and standard deviation satisfy