32 citations · 51 across the 14 of their papers we have counts for
15 papers
Bivariate asymptotics via random walks: application to large genus maps
Andrew Elvey Price, Wenjie Fang, Baptiste Louf +1
We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two r…
Modularity and Graph Expansion
Baptiste Louf, Colin McDiarmid, Fiona Skerman
We relate two important notions in graph theory: expanders which are highly connected graphs, and modularity a parameter of a graph that is primarily used in community detection. M…
Distances and isoperimetric inequalities in random triangulations of high genus
Thomas Budzinski, Guillaume Chapuy, Baptiste Louf
We prove that uniform random triangulations whose genus is proportional to their size have diameter of order with high probability. We also show that in such triangula…
Random partitions under the Plancherel-Hurwitz measure, high genus Hurwitz numbers and maps
Guillaume Chapuy, Baptiste Louf, Harriet Walsh
We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural…
The Discrete Gaussian model, I. Renormalisation group flow at high temperature
Roland Bauerschmidt, Jiwoon Park, Pierre-François Rodriguez
The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that its macroscopic s…
Unicellular maps vs hyperbolic surfaces in large genus: simple closed curves
Svante Janson, Baptiste Louf
We study uniformly random maps with a single face, genus , and size , as with , in continuation of several previous works on the geometric p…
Random generation and scaling limits of fixed genus factorizations into transpositions
Valentin Féray, Baptiste Louf, Paul Thévenin
We study the asymptotic behaviour of random factorizations of the -cycle into transpositions of fixed genus . They have a geometric interpretation as branched covers of the…
Short cycles in high genus unicellular maps
Svante Janson, Baptiste Louf
We study large uniform random maps with one face whose genus grows linearly with the number of edges, which are a model of discrete hyperbolic geometry. In previous works, several…
Large expanders in high genus unicellular maps
Baptiste Louf
We study large uniform random maps with one face whose genus grows linearly with the number of edges. They can be seen as a model of discrete hyperbolic geometry. In the past, seve…
Finding large expanders in graphs: from topological minors to induced subgraphs
Baptiste Louf, Fiona Skerman
In this paper, we consider a structural and geometric property of graphs, namely the presence of large expanders. The problem of finding such structures was first considered by Kri…
Local limits of bipartite maps with prescribed face degrees in high genus
Thomas Budzinski, Baptiste Louf
We study the local limits of uniform high genus bipartite maps with prescribed face degrees. We prove the convergence towards a family of infinite maps of the plane, the q-IBPMs, w…
Planarity and non-separating cycles in uniform high genus quadrangulations
Baptiste Louf
We study large uniform random quadrangulations whose genus grow linearly with the number of faces, whose local convergence was recently established by Budzinski and the author arXi…
Simple formulas for constellations and bipartite maps with prescribed degrees
Baptiste Louf
We obtain simple quadratic recurrence formulas counting bipartite maps on surfaces with prescribed degrees (in particular, -angulations), and constellations. These formulas are…
Local limits of uniform triangulations in high genus
Thomas Budzinski, Baptiste Louf
We prove a conjecture of Benjamini and Curien stating that the local limits of uniform random triangulations whose genus is proportional to the number of faces are the Planar Stoch…
A new family of bijections for planar maps
Baptiste Louf
We present bijections for the planar cases of two counting formulas on maps that arise from the KP hierarchy (Goulden-Jackson and Carrell-Chapuy formulas), relying on a "cut-and-sl…