4 problems

Let $\mathcal{T}_{n,g}$ be the set of rooted triangulations of genus $g$ with $n$ vertices, and let $T_{n,g}$ be uniformly distributed in $\mathcal{T}_{n,g}$. For…

Fix $\kappa\in(0,\frac{2}{27}]$, and let $\mathbf{T}_{\kappa}$ be the corresponding infinite triangulation. Let $T_{n,g}$ be a uniformly rooted triangulation of genus $g$ with $n$…

For $g\geq 0$, let $\mathcal{T}_{n,g}$ be the set of rooted triangulations of the torus of genus $g$ with $n$ vertices, and let $T_{n,g}$ be uniformly distributed in…

The paper constructs a family of random infinite triangulations, and let $T_{n,g}$ denote a uniformly chosen rooted triangulation of genus $g$ with $n$ vertices. Local-limit conjec…