9 problems

Let $c4_N$ denote the distribution of the relevant finite planar triangulations, conditioned to have all vertex degrees bounded by $M$. Weak convergence conjecture. For every…

Conditional non-degeneracy conjecture. For fixed $k\geq 2$, the conditional distribution of $\alpha(\mathcal W_{d+k,d})$ converges weakly as $d\to\infty$ to a limit law not concent…

The absence conjecture. There is no normed linear space where an unbounded sequence converges $d$-weakly.

Let $t\in\mathbb{N}$, let $\psi\in\mathcal{B}_b(\mathbb{R}^{t+2})$ be continuous, and let $h\in\mathcal{B}_b(\mathbb{R}^{d(t+1)})$. For the step-$n$ particles $X_n^{M,m}$, define ……

For the birth Mallows process, let $J_t=|\{k\leq\binom{n}{2}:T_k\leq t\}|$ be the number of jumps by time $t$. Gaussian Markov-limit conjecture. As $n$ tends to infinity, … where…

Density conjecture. The class of QID distributions on $\mathbb{R}^{d}$ with finite quasi-Lévy measure and zero Gaussian variance is dense in the space of probability distributions…

Conditional geometric-limit conjecture. Conditionally on $X_n\ne0$, the random variable $X_n$ converges weakly to a random variable $Y_\infty$ satisfying

Let $\eta_t$ be the bias voter model on $S$, where $S=\mathbb{T}^d$ or $S=\mathbb{Z}^d$ with $d\geq 1$, started from the product initial distribution $\mu_p$ with $p\in (0,1)$. Wea…

Let $\mathfrak d(z)=\sum_{i=1}^k Q_i(z)\frac{d^i}{dz^i}$ be a non-degenerate higher Lamé operator, and let $r=\max_{i=1,\ldots,k}(\deg Q_i-i)$. Let $Pol_r$ be the space of monic po…