9 problems

Let $bbL$ be a family of iterated function systems satisfying the UOSC and Condition. Let $bbP$ be a random code-tree measure, and assume that $F_\tau$ is not almost deterministic.…

Let $K\subset\mathbb{R}$ be a nonrandom compact set, let $\mathfrak S(\theta)$ be the random set of points of slow growth at parameter $\theta$, and let $\lambda(\theta)$ denote th…

Let $u$ be a probability measure on $\mathbb{R}^d$, let $(omegak){k=1}^{\infty}$ be independent random points distributed according to $nu$, and for $\alpha0$ define … Write…

For each $\underline{\kappa}\in(0,4)$, let $\rho_c=\rho_c(\underline{\kappa})$ lie in $(-2-\underline{\kappa}/2,-2)\cap[\underline{\kappa}/2-4,-2)$, and let $\eta$ be an SLE…

For $\kappa \in (4,8)$, let $\eta$ be an SLE$_\kappa$ curve from $0$ to $\infty$ in $\mathbb{H}$. The adjacency graph of the connected components of $\mathbb{H} \setminus \eta$ has…

Positive critical Hausdorff measure conjecture. With probability one with respect to $\mu_{\mathbf{p}}$,

A uniformly random self-affine set is obtained as the attractor of a random iterated function system of affine contractions, with the randomness specified by the model under consid…

Whole-plane SLE reversibility conjecture. The whole-plane SLE$_\kappa$ trace satisfies reversibility for $\kappa\in(0,4]$.

Let $\bar\beta(t)$ denote the average spectrum of SLE, and let $t_{\min}$ and $t_{\max}$ be the two points such that a tangent to $\bar\beta(t)$ intersects the $y$-axis at $-1$. The…