High order expansion of matrix models and enumeration of maps

利用Dumitriu-Edelman模型对地图的枚举

Enumeration of maps with the Dumitriu-Edelman model

利用Dumitriu-Edelman三对角模型，给出了β系综粒子幂和累积量在1/N和β下的展开，系数由Bouttier、Fusy和Guitter引入的适当标记地图表示，仅涉及可定向地图，并通过新映射将前两阶与LaCroix的展开联系起来。

Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants

We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively by Collet and Fusy. In this paper, we obtain an even simpler formula for \emph{tight} pairs of pants, namely for maps whose boundaries have minimal length in their homotopy class. We follow a bijective approach based on the slice decomposition, which we extend by introducing new fundamental building blocks called bigeodesic triangles and diangles, and by working…

The local limit of unicellular maps in high genus

We show that the local limit of unicellular maps whose genus is proportional to the number of edges is a supercritical geometric Galton-Watson tree conditioned to survive. The proof relies on enumeration results obtained via the recent bijection given by the second author together with Feray and Fusy.

从平面地图的边界度量看双尺度SYK模型

Double-scaled SYK from boundary metrics of planar maps

本文研究一类具有特殊q变形面权重的二分平面地图模型，证明其边界度量枚举仅依赖于测地线弦图的交叉数，并与双尺度SYK模型的弦图表示一致。

Tessellations of random maps of arbitrary genus

We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing to encode such structures into labeled maps with a fixed number of faces. We investigate the scaling limits of the latter. Applications include asymptotic enumeration results for quadrangulations, and typical metric properties of randomly sampled quadrangulations. In particular, we show that scaling limits of these random quadrangulations are such that almost every pair of points are linked by a unique geodesic…

具有紧边界的地图计数及Zhukovsky变换

Enumeration of maps with tight boundaries and the Zhukovsky transformation

本文研究了具有紧边界的地图生成函数，揭示其与Zhukovsky变换的关系，并在二部情况下给出了显式公式，同时推导了递推关系。