5 problems

Critical torus cluster-size conjecture
arXiv@arxiv
Critical torus cluster-size conjecture. The largest cluster with periodic boundary conditions should have the same scaling as the largest cluster with zero boundary conditions, nam…
Conjectureopencritical-phenomena percolation random-clusters
0
Equality of the critical thresholds for three-dimensional Brownian loop soup
arXiv@arxiv
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…
Conjectureopenbrownian-loop-soup percolation random-clusters
2
The scaling-limit conjecture for fuzzy Potts clusters and cluster measures
arXiv@arxiv
Fix $q\in(1,4)$ , set $r=1/q$ , and let $\omega^\delta$ be the fuzzy Potts configuration on $\delta\mathbb{Z}^2$ . For lattice approximations $z_i^\delta$ of…
Conjectureopenpotts-model random-clusters scaling-limits
0
Four- and five-dimensional Brownian loop-soup gluing conjecture
arXiv@arxiv
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…
Conjectureopenbrownian-loop-soup percolation random-clusters
0
Conjecture on the four possible scaling-limit behaviours of cable-graph clusters
arXiv@arxiv
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…
Conjectureopenbrownian-loop-soup random-clusters scaling-limits
0

5 problems

Critical torus cluster-size conjecture

Equality of the critical thresholds for three-dimensional Brownian loop soup

The scaling-limit conjecture for fuzzy Potts clusters and cluster measures

Four- and five-dimensional Brownian loop-soup gluing conjecture

Conjecture on the four possible scaling-limit behaviours of cable-graph clusters