4 papers
High genus one part monotone Hurwitz numbers
Simon Barazer, Baptiste Louf
We obtain bivariate asymptotics for one part monotone Hurwitz numbers in high genus (i.e. as both the size and the genus go to infinity). To do so, we start with a linear recurrenc…
Volumes of moduli spaces of directed ribbon graphs and Cut-and-Join operators
Simon Barazer
In this paper, we investigate the algebraic structure underlying the acyclic decomposition. This decomposition applies to directed metric ribbon graphs and enables the recursive co…
Average diffusion rate of Ehrenfest Wind-tree billiards
Simon Barazer
One of the versions of the wind-tree model of Boltzmann gas, suggested by Paul and Tatiana Ehrenfest more than a century ago, can be seen as a billiard in the plane endowed with $\…
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…