13 problems

Extremal-process moderate-deviation conjecture. As $n\to\infty$,

Neeman–Radin–Sadun's conjecture. The lower-tail probability satisfies

Let $S(P)$ denote the channel skewness for the Gaussian channel, let $Q^{-1}(epsilon)$ be the inverse Gaussian tail function at error probability $epsilon$, and consider the achiev…

Let $R$ satisfy $R\in(2,\frac12L)$, and let $B_R$ be the disc of radius $R$, with halo volume $V(\gamma)$ under the probability measure $\mu_\beta$. Write $I(B_R)$ for the halo rat…

The Poisson-binomial improvement conjecture. The bound in Poisson-binomial approximation can be significantly improved, with the better estimate likely depending on the displayed R…

Let $A_n$ be the companion matrices of the stable but nearly unstable processes considered in the paper, and let $\rho(A_n)$ denote their spectral radius. The discussion concerns t…

Extended general structure conjecture. The projected coefficient satisfies

Let $M^*(\mathcal{W};n,\varepsilon_n)$ denote the maximal number of messages transmissible over the quantum channel $\mathcal{W}$ using $n$ channel uses with error probability…

Self-normalized moderate deviation conjecture. The two displayed approximations hold in the stated ranges of $x$. These estimates would extend precise moderate-deviation results fo…

Moderate deviation conjecture. The moderate deviation principle may still hold for $V^n(X)$ in this setting, although the corresponding large deviation principle is not expected to…

Studentized statistics are ratios used to account for heteroscedasticity and improve robustness to heavy-tailed data, and resampling methods based on them are considered in statist…

Let $X_1,X_2,\ldots$ be identically distributed random variables with $\mathsf{E}X_1=0$, set $S_k=\sum_{i=1}^k X_i$ and $V_n=(\sum_{i=1}^n X_i^2)^{1/2}$, and let $\Phi$ denote the…

Queueing systems can be studied under heavy-traffic diffusion approximations and under large-deviation asymptotics; the moderate-deviation (MD) scale lies between these regimes. In…