39 citations · 85 across the 15 of their papers we have counts for
5 papers · 1 filter
The diameter of random Belyi surfaces
Thomas Budzinski, Nicolas Curien, Bram Petri
We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. This model consists of a uniform gluing of hyperbo…
Kissing numbers of regular graphs
Maxime Fortier Bourque, Bram Petri
We prove a sharp upper bound on the number of shortest cycles contained inside any connected graph in terms of its number of vertices, girth, and maximal degree. Equality holds onl…
On the minimal diameter of closed hyperbolic surfaces
Thomas Budzinski, Nicolas Curien, Bram Petri
We prove that the minimal diameter of a hyperbolic compact orientable surface of genus is asymptotic to as . The proof relies on a random construction, w…
Kissing numbers of closed hyperbolic manifolds
Maxime Fortier Bourque, Bram Petri
We prove an upper bound for the number of shortest closed geodesics in a closed hyperbolic manifold of any dimension in terms of its volume and systole, generalizing a theorem of P…
Universality for random surfaces in unconstrained genus
Thomas Budzinski, Nicolas Curien, Bram Petri
Starting from an arbitrary sequence of polygons whose total perimeter is , we can build an (oriented) surface by pairing their sides in a uniform fashion. Chmutov and Pittel (a…