10 problems

Let a biased random walk on dynamical percolation be given in the setting of Proposition, and let an annealed invariance principle hold for its scaling limit. A quenched invariance…

Weak-dependence conjecture. Some time series satisfy weak dependence conditions with fast enough decay rates to ensure a Donsker type theorem, but satisfy neither condition nor ano…

Infinite-horizon Lorentz-process conjecture. As $N\to\infty$,

Let $N$ be the number of particles, let $\beta$ denote the branching parameter, and let $\mu_c^N$ be the critical drift for the $N$-particle Brownian bees system. For a drift $\mu$…

All-temperature invariance-principle conjecture. The paper's invariance principle holds for all $\beta>0$, including the low-temperature regime, when

Quenched scaling conjecture. For almost every such $\rho$,

Let $d\geq 3$ and consider the long-range percolation graph on $\mathbb Z^d$ with connection probabilities having the asymptotic decay specified by the paper for some $s>d+2$. A qu…

Multiplicative separability conjecture. For all positive definite attributes $A$, whenever $U$ belongs to $\mathcal{G}$, the contrast is multiplicatively separable and

Let $f$ be a harmonic multilinear polynomial, and let $f(\nu_{pn})$ and $f(\mu_p)$ denote its distributions under the uniform measure on the slice of the Boolean cube with paramete…

Let $(g_n)$ be regularly varying with index $\gamma-1$, and suppose the stable-domain assumptions and the relevant process definitions are those of Theorems $\GammaGTOne$ and…