2021/04/27 by Daniel Amankwah, Amankwah, Daniel, Sigurður Örn Stefánsson +1
Computer Science · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2104.13364
openalex publication_date 2021/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider maps which are constructed from plane trees by assigning marks to the corners of each vertex and then connecting each pair of consecutive marks on their contour by a single edge. A measure is defined on the set of such maps by assigning Boltzmann weights to the faces. When every vertex has exactly one marked corner, these maps are dissections of a polygon which are bijectively related to non-crossing trees. When every vertex has at least one marked corner, the maps are outerplanar and each of its two-connected component is bijectively related to a non-crossing tree. We study the scaling limits of the maps under these conditions and establish that for certain choices of the weights the scaling limits are either the Brownian CRT or the α-stable looptrees of Curien and Kortchemski.