2 papers
math.PR2023
Length spectrum of large genus random metric maps
Simon Barazer, Alessandro Giacchetto, Mingkun Liu
We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach. We establish that, as the genu…
math.GT2023
Random surfaces with large systoles
Mingkun Liu, Bram Petri
We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their are…