11 problems

For $0\le n<2$, let $c(n)$ denote the central charge associated with colored doodles. Model II universality conjecture. Colored doodles are in the universality class of models with…

Harmonic-map metastability conjecture. The relaxation time of the corresponding Langevin dynamics grows exponentially fast with $\beta$ if and only if $\mathcal E$ has non-trivial,…

Polynomial relaxation-time conjecture. For all lattice dimensions $d\geq 2$, all $N\geq 2$, and arbitrary boundary conditions, the relaxation time is at most of order $L^d$ at any…

Le Gall–Miermont's supercritical gasket conjecture. If $h>h_c(N)$, the gasket of a large random decorated triangulation under $P_{g,h,N}$ converges, after suitable scaling, towards…

Le Gall–Miermont's subcritical gasket conjecture. There exists $h_c(N)$ such that, if $h<h_c(N)$, the scaling limits of random planar decorated triangulations and of their gaskets…

Consider the $O(n)$ model on the hexagonal lattice with $n\in[0,2)$, and let … Dense-phase O(n) interface conjecture. As the lattice step tends to zero, the law of the $O(n)$ inter…

Consider the $O(n)$ model on the hexagonal lattice with $n\in[0,2)$ and critical edge-weight … Dilute-phase O(n) interface conjecture. As the mesh size tends to zero, the law of th…

Consider the $O(n)$ model on the hexagonal lattice with $n\in[0,2]$, and let $(\Omega,a,b)$ be a simply connected domain with two boundary points. Set … Let $F_\delta$ be the paraf…

Consider the $O(n)$ model on the hexagonal lattice with loop-weight $n\in(0,2)$ and edge-weight $x>0$, and define … Nienhuis's BKT conjecture. For $x<x_c(n)$, the probability that…

External-gasket conformal-loop conjecture. The external gasket of $O(N)$ models should converge to conformal loop ensembles.

O(N) critical-exponent conjecture. There exists a function $x_c(\beta)>0$ and a critical value $\beta_c>0$ such that, for fixed $\beta>\beta_c$ and $x=x_c(\beta)$,