10 problems

Linear cumulant conjecture. Every cumulant is a linear function of $n$ for all $k\geq 1$.

Let $C_{k,m,n}$ be the minimum cost of a $k$-matching in the random bipartite matching model, and let its cumulants $\kappa_p$ be defined by … where…

Let $T_r$ denote the correction to the $r$th cumulant of $X^{(n)}_3$ arising from dependence among the pair indicators. Cumulant-correction conjecture. … The surrounding argument e…

Let $F_\infty$ be the target random variable in the second Wiener chaos of the form referenced in the source, and let $F=I_q(f)$ be a chaotic random variable in the $q$th Wiener ch…

Cumulant-coefficient positivity conjecture. For partitions $cpi_1,\dots,cpi_\ell$, the polynomial $(-1)^{\ell-1}d^\sigma_{\pi_1,\dots,\pi_\ell}(cdelta)$ has non-negative integer co…

Kerov–Lassalle cumulant-positivity conjecture. For all integers $k_1,\dots,k_\ell\geq 1$, the polynomial which expresses this signed cumulant in terms of…

Let $\lambda^1,\dots,\lambda^r$ be partitions. For $I\subseteq [r]$, let $\lambda^I$ denote the combined partition used in the Macdonald polynomial $J_{\lambda^I}^{(q,t)}$, and let…

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 ……

Cumulant conjecture. The right-hand side of this relation must be related to the $p$th cumulant of the $p$th moment of the mean spectral distribution of $M$, and this relation shou…

Let $\b7$?