论文标题
均匀高属四边形的平面性和非分离周期
Planarity and non-separating cycles in uniform high genus quadrangulations
论文作者
论文摘要
我们研究了大型均匀的随机四边形，其属与面孔的数量线性生长，该属的局部收敛最近由Budzinski和作者Arxiv：1902.00492，Arxiv：2012.05813。在这里，我们研究了这些物体的几种属性，这些属性未被局部拓扑捕获。也就是说，我们表明根周围的球是平面WHP到对数半径，并且证明存在阳性概率的短循环。
We study large uniform random quadrangulations whose genus grow linearly with the number of faces, whose local convergence was recently established by Budzinski and the author arXiv:1902.00492,arXiv:2012.05813. Here we study several properties of these objects which are not captured by the local topology. Namely we show that balls around the root are planar whp up to logarithmic radius, and we prove that there exists short non-contractible cycles with positive probability.
