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We study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [ 9 ,… Click to show full abstract
We study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [ 9 , 10 ]. 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 with high probability up to logarithmic radius, and we prove that there exist non-contractible cycles of constant length with positive probability.
Keywords:
planarity non;
genus;
cycles uniform;
separating cycles;
non separating;
uniform high
Journal Title: Probability Theory and Related Fields
Year Published: 2021
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Journal Title: Probability Theory and Related Fields
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!