7 problems

Fix $m\geqslant2$ and $\delta>0$. Let $T_n$ be the number of triangles in the instantaneous variant of the linear preferential attachment model, with connections specified by the i…

Consider the setting of Theorem Trate: a constrained or unconstrained U-statistic built from the random sequence and kernel in the paper, with Kolmogorov distance $d_K$ and the the…

Let $p$ be a positive integer and let $W=\sum_{i\in I}X_i$, where ${\mathbbm{E}}X_i=0$, ${\mathbbm{E}}W^2=1$, and the variables satisfy (LD1)--(LD$(p+1)$): for each $i_1\in I$,…

Let $X$ be a multiple Wiener--Itô integral of order $p\geq 2$, and let $\kappa_6(X)$ denote its sixth cumulant. Sixth-cumulant positivity conjecture. For every such $X$, one has ……

Let $k,l\geq 2$ be distinct positive integers, and let $\{X_n\}_{n\geq 1}$ be a sequence of eigenfunctions lying in the same eigenspace of a Markov generator $\mathrm{\mathbf L}$ s…

Let $M$ be a binomially or Poisson-distributed random variable with $G$-transform $G(M)$, and let $\Phi$ denote the standard Gaussian distribution function. The increasing property…

Let $M$ be a binomially distributed or Poisson-distributed random variable, let $P_0$ be its distribution, and let $G(M)$ be its $G$-transform, defined by assigning the signed squa…