Distance statistics in quadrangulations with no multiple edges and the geometry of minbus. (English) Zbl 1198.05034
A bijection between quadrangulations and well-labeled trees is used to study distance statistics. Several generating functions are used to specify the law for the distance between randomly selected edges or vertices in different types of quadrangulations. Local limit laws are given for large quadrangulations with no multiple edges. Extensions to general quadrangulations are discussed.
Reviewer: Ove Frank (Stockholm)
MSC:
| 05C12 | Distance in graphs |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 05C05 | Trees |
| 05A15 | Exact enumeration problems, generating functions |
| 60G50 | Sums of independent random variables; random walks |
| 05C63 | Infinite graphs |
