18 problems

Let $T$, $B$, $F$, and $C$ be the four random variables defined in the depth-first search analysis of the random digraph. Joint asymptotic normality conjecture. All four variables…

Let $\sigma$ be a primitive substitution of constant length $d$ with eigenvalue $1$ and eigenvector $\gamma$. Write $S_{\lfloor d^n t\rfloor}(\gamma)$ for the associated ergodic su…

Consider the random location deaths (RLD) process with birth probability $p$, death probability $q=1-p$, and parameter $r$. Let $L_n(a)$ be the number of species alive at time $n$…

Let $K_2(X)$ be the Farey set of elements $a/c$ in the class-number-one imaginary quadratic field with discriminant parameter $D=2$ and $|c|^2<X$, and let … For the normalized elli…

Let $T_n$ be the triangle count under the edge-triangle model with law ${\mathbb P}_{n;\alpha,h}$, and let $(\alpha_c,h_c)$ be the critical parameter pair. At this pair, let…

Baird–Epstein–Flint–Miller Gaussianity conjecture. As $N\to\infty$, the distribution of the game length converges to a Gaussian distribution, with expectation and variance approxim…

Recursive limit-law conjecture. The limit law of $F$ is determined recursively as follows. If $P$ is a normal pattern, then $F$ is a Poisson pattern; in all other cases for $P$,…

Higher-order limit conjecture. The conclusion of Theorem nCLT continues to hold if $p\geq 3$; that is, as $n\to\infty$,

Let $Z$ be the number of occurrences of a pattern $w$ as a subsequence in a random text of length $n$, and let $\binom{n}{m}$ be the number of possible positions for a subsequence…

Free-to-Boolean maximum convergence conjecture. Then there exists $G\in\Delta_+$ such that

Let $X_t$ be the mass variable of the continuous-time Derrida–Retaux model started from $\mu_0$, and let $\mathcal{L}(X_t\mid X_t>0)$ denote its conditional law given positivity. C…

Let $X^*$ be the process considered in Theorem, and let $\alpha$ be the parameter appearing in the regular-variation assumption. The theorem currently assumes that $\alpha$ is an i…

Let $x=\{x_n,n\in\textbf N\}\in\textbf Z_2$ be a point, and let $t_n(x)$ be the ordinal number of its length-$n$ initial fragment among the binary sequences of length $n$ having th…

Let a cyclic polling system have general renewal arrival processes and deterministic switch-over times. The system is considered in the regime where the deterministic switch-over t…

Let $\gamma\in(\frac12,1)$, let $v:X\to\mathbb{R}^d$ and $h:X\to G$ be the observable and cocycle from the system, and let $\operatorname{Fix} h(0)=\{w\in\mathbb{R}^d:h(0)w=w\}$. W…

Let $X_n$ and $Y_n$ be the random variables defined in the paper, representing the relevant crossing statistics on set partitions. Asymptotic Gaussianity conjecture. The distributi…

Extension conjecture. The special SRD and LRD mixed-case limit theorem holds without the restriction that $k_{j,L}$ be $1$ or $2$; in particular,

Local limit conjecture. Uniformly for all choices of $a_1,\dots,a_m$ and all integers $k$,