19 problems

Let $c{lambda}$ and $c{phi}$ be regularly varying random variables, with tail exponents $calpha$ and $cbeta$, respectively. Let $A$ and $B$ be random matrices in general position,…

Let $\mathcal{D}^-$ be the class of distributions considered in the paper, and let $\mathcal{S}_C$ denote the class of super-Cauchy distributions. Super-Cauchy characterization con…

Dependence conjecture. $Z_n$ and $N_n$ will not be asymptotically independent anymore. The conjecture concerns the joint limit behavior of the standardized trace and the point proc…

Scale-free infinity-PageRank conjecture. If $d_i\sim X$ where $X$ is a regularly varying random variable, then $PR_\infty(i)$ will also be scale-free.

Weak Conjecture. The runtime of $texttt{Alfa}$ with $texttt{SLS} in { texttt{SRWA}, texttt{probSAT}, texttt{YalSAT} }$ is long-tailed.

Consider normalizing flows built from NSF layers, where the tails of each NSF layer are linear. Tail-linearity conjecture. The observed improved performance in low-sample tail regi…

Tail-asymptotics conjecture. Under this moment bound, for $y>0$,

Let $\mathbb{G}_n$ and the uniformly chosen vertices $U_{n,1},U_{n,2}$ be as in Theorem … , there is a constant $\varepsilon_{\ast}\in(0,1)$ depending on the model parameters such…

Stability conjecture. The tail-index results should be valid whenever the original fork-join model is stable.

Let $X_1,\ldots,X_L$ be independently (not necessarily identically) distributed random matrices with heavy tails and unitary invariance, meaning that their eigenvalues and eigenvec…

Consider the fixed-point branching process with state-independent immigration represented as … where $A_1=A$, the variables $\{A_i\}$ are independent and identically distributed, a…

Let $B_i$ denote the busy period associated with class $i$, let $F$ be the reference service-time distribution with tail ${\overline F}(x)=1-F(x)$, and let $d_i$ be the coefficient…

The paper considers linear state-space models with Gaussian measurement noise and state-equation noises whose components have alpha-stable distributions with parameters alpha and b…

Let $H$ be an infinitely divisible distribution, and let the distribution generated by its Lévy spectral measure be denoted by $F_H$. Let $\mathcal{L}(\gamma)$, for $\gamma\ge0$, d…

Let $F$ be a distribution, let $F^{*n}$ denote its $n$-fold convolution, and let $p_n\ge0$ satisfy … The corresponding compound distribution is $\sum_{n=0}^{\infty}p_nF^{*n}$. Let…

Let $\mathcal{J}$ denote the class of distributions obeying the principle of a single big jump, let $\mathcal{K}$ be the class of heavy-tailed distributions, and let…

Let task deadlines follow the Pareto distribution described above, with parameter $\omega\leq 2$, so that no moments of the deadline distribution exist. Timely-delivery conjecture.…

Power-law dominance conjecture. Power-law distributions, particularly those based on self-organized critical models, rather than commonly used Gaussian-like exponential forms, coul…

Let $r>0$, and let $D$ be the ambient dimension. Consider any distribution on unit vectors in a $D$-dimensional space whose $\psi_r$ norm is at most $O(1/\sqrt{D})$. Let $M$ be the…