12 problems

Fix $c\in(0,1)$. Let $\mathcal L_D^c$ be a Brownian loop soup of central charge $c$, let $\mathcal C$ be one of its clusters, and let $:\mathtt h_c\Theta_{\mathcal L_D^c}^{n-1}:$ d…

Let $\lpha_c$, $\lpha_u$, $\lpha_{\rm tr}$, and $\lpha_{\mathop{\rm b2b}}$ denote the thresholds defined in the paper for, respectively, percolation, uniqueness, truncated-model pe…

Let $\mathbf{c}in(0,1]$ be the intensity of a critical Brownian loop soup, and let $xi_{\mathbf{c}}(2)$ and $xi_{\mathbf{c}}(4)$ denote the generalized disconnection exponents intr…

Let $\kappa_c\in(4,8)$ be the critical parameter from the source's SLE conjecture on conformal removability and bubble connectivity, and let scenario denote the second scenario in…

Camia's massive loop-soup conjecture. The outer boundaries of the outermost clusters of the massive Brownian loop soup at intensity $1/2$ should be distributed as the level lines o…

Let $\theta>1$ and let $\tau\geq 0$. Let $\mathcal{L}_{\mathtt{C},\tau}^\theta$ denote the collection of loops in the Brownian loop soup whose duration is at least $\tau$. Unbounde…

Let $\mathcal{T}$ denote the boundary stress-energy tensor of the Brownian loop soup, and let the 2-leg operator be the boundary operator of the $O(0)$ model associated with two se…

One-point loop-soup insertion conjecture. Similarly to the two-point relation, one has

For $d\geq4$, consider the Brownian loop-soup in $(0,1)^d$ and the operation of contracting each loop, so that percolation can be viewed as a mechanism for gluing loops into cluste…

Let $d\in\{4,5\}$, and consider the cable-graph clusters in $(0,1)^d\cap\delta\mathbb Z^d$ as $\delta\to0$. Four- and five-dimensional scaling-limit conjecture. The limit in distri…

Let $d=3$, and let the cable-graph loop-soup clusters be formed on finer and finer meshes. Denote by $\Delta$ the Hausdorff dimension of the Brownian loop-soup clusters. Three-dime…

Consider the four scenarios for the fine-mesh limit of cable-graph loop-soup clusters: no limiting joint law; convergence to the macroscopic Brownian loop-soup clusters; agglomerat…