10 problems

Let $\mu$ be a CNA+ measure, and condition it on the total rank $\sum_eX_e$. Rank-cover conjecture. For each $k$, the conditional distribution given total rank $k+1$ stochastically…

Let $T_n(f)$ be the preferential attachment tree on $[n]$ generated by the nondecreasing attachment function $f:{\mathbb{N}}_0\to\mathbb{R}_{>0}$. Write $D_n(f)$ for the graph dist…

Stochastic diameter monotonicity conjecture. If

Let $n>1$ and consider the distance from a typical general vehicle to its $n$th-nearest neighbor in the PLM-PPP and in the PSP-PPP, with Rayleigh-distributed half-lengths. Nearest-…

Best-systems conjecture. Regardless of the message-size distribution,

Let $p$ and $q$ be symmetric unimodal weight functions, meaning that $i\mapsto p(i)$ and $i\mapsto q(i)$ are symmetric and decreasing for $i\geq0$. Let $p\preceq_Mq$ denote majoriz…

Let $Q_1^b(\infty)$, $Q_1^h(\infty)$ and $Q_1^c(\infty)$ denote the stationary numbers of needy patients in the Erlang-R models with blocking and holding and in the closed ward mod…

Let $f$ be a nonzero quadratic form and let $\Sigma$ be a nonzero positive semidefinite matrix. Write $W_{f,\Sigma}$ for the corresponding Wald random variable. Quadratic lower-bou…

Let $\mu$ be a probability measure on $\{0,1\}^n$. Say that $\mu$ has the stochastic covering property (SCP) if, for every coordinate $i$, the conditional law given $\eta_i=0$ stoc…

Let $\mu$ be a probability measure on $\{0,1\}^n$. Write $\mu_k$ for the conditional measure given $\sum_i\eta_i=k$, and say that $\mu$ has the normalized matching property (NMP) w…