8 problems

Feng–Hu conjecture. The degree probabilities satisfy

Global fractional-linear bound conjecture. The inequality

Let $X\in\{0,\ldots,n\}$ be a random variable with $p_0p_n>0$ and probability generating function $f_X$. Let $\delta>0$ and $R\geqslant1$. If every zero $\zeta$ of $f_X$ satisfies…

Pemantle's conjecture. If $\sigma(X)\gg1$, then $X$ is approximately normally distributed. This conjecture was the original motivation for studying anti-concentration from zero-fre…

Let $X$ be a strongly Rayleigh random variable, and let $j,k\geq 1$. Write $\left\lfloor jX/k\right\rfloor$ for the integer-valued floor of $jX/k$. Poisson multinomial decompositio…

Pemantle's conjecture. If $\sigma_n\rightarrow\infty$, then

Modified Pemantle conjecture. If

Let $X_n$in$\{0,\ldots,n\}$ be a sequence of random variables with probability generating functions $P_n(z)$ and variance $sigma_n^2$. Assume that all roots of $P_n(z)$ avoid a nei…