52 citations · 402 across the 46 of their papers we have counts for
47 papers
Composition of random functions and word reconstruction
Guillaume Chapuy, Guillem Perarnau
Given two functions and chosen uniformly at random, any word induces a…
On the scaling of random Tamari intervals and Schnyder woods of random triangulations (with an asymptotic D-finite trick)
Guillaume Chapuy
We consider a Tamari interval of size (i.e., a pair of Dyck paths which are comparable for the Tamari relation) chosen uniformly at random. We show that the height of a uniform…
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…
A telescopic proof of Cayley's formula
Guillaume Chapuy, Guillem Perarnau
We give a short proof of the fact that the number of labelled trees on vertices is . Although many short proofs are known, we have not seen this one before.
On the edge-density of the Brownian co-graphon and common ancestors of pairs in the CRT
Guillaume Chapuy
Bassino et al. (arXiv:1907.08517) have shown that uniform random co-graphs (graphs without induced ) of size converge to a certain non-deterministic graphon. The edge-dens…
Note on the density of ISE and a related diffusion
Guillaume Chapuy, Jean-François Marckert
The integrated super-Brownian excursion (ISE) is the occupation measure of the spatial component of the head of the Brownian snake with lifetime process the normalized Brownian exc…
Topological recursion for Orlov-Scherbin tau functions, and constellations with internal faces
Valentin Bonzom, Guillaume Chapuy, Séverin Charbonnier +1
We study the correlators arising from Orlov-Scherbin 2-Toda tau functions with rational content-weight , at arbitrary values of the two sets of time parameters. Com…
Short Synchronizing Words for Random Automata
Guillaume Chapuy, Guillem Perarnau
We prove that a uniformly random automaton with states on a 2-letter alphabet has a synchronizing word of length with high probability (w.h.p.). That is to s…
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…
Enumeration of non-oriented maps via integrability
Valentin Bonzom, Guillaume Chapuy, Maciej Dołęga
In this note, we examine how the BKP structure of the generating series of several models of maps on non-oriented surfaces can be used to obtain explicit and/or efficient recurrenc…
Counting chains in the noncrossing partition lattice via the W-Laplacian
Guillaume Chapuy, Theo Douvropoulos
We give an elementary, case-free, Coxeter-theoretic derivation of the formula for the number of maximal chains in the noncrossing partition lattice of a real re…
-monotone Hurwitz numbers: Virasoro constraints, BKP hierarchy, and -BGW integral
Valentin Bonzom, Guillaume Chapuy, Maciej Dołęga
We study a -deformation of monotone Hurwitz numbers, obtained by deforming Schur functions into Jack symmetric functions. We give an evolution equation for this model and derive…
Coxeter factorizations with generalized Jucys-Murphy weights and Matrix Tree theorems for reflection groups
Guillaume Chapuy, Theo Douvropoulos
We prove universal (case-free) formulas for the weighted enumeration of factorizations of Coxeter elements into products of reflections valid in any well-generated reflection group…
Non-orientable branched coverings, -Hurwitz numbers, and positivity for multiparametric Jack expansions
Guillaume Chapuy, Maciej Dołęga
We introduce a one-parameter deformation of the 2-Toda tau-function of (weighted) Hurwitz numbers, obtained by deforming Schur functions into Jack symmetric functions. We show that…
On the number of coloured triangulations of -manifolds
Guillaume Chapuy, Guillem Perarnau
We give superexponential lower and upper bounds on the number of coloured -dimensional triangulations whose underlying space is an oriented manifold, when the number of simplice…
Weighted Hurwitz numbers and topological recursion
A. Alexandrov, G. Chapuy, B. Eynard +1
The KP and 2D Toda tau-functions of hypergeometric type that serve as generating functions for weighted single and double Hurwitz numbers are related to the topological recursion p…
Fermionic approach to weighted Hurwitz numbers and topological recursion
A. Alexandrov, G. Chapuy, B. Eynard +1
A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and…
Weighted Hurwitz numbers and topological recursion: an overview
A. Alexandrov, G. Chapuy, B. Eynard +1
Multiparametric families of hypergeometric -functions of KP or Toda type serve as generating functions for weighted Hurwitz numbers, providing weighted enumerations of branched…
Local convergence and stability of tight bridge-addable graph classes
Guillaume Chapuy, Guillem Perarnau
A class of graphs is bridge-addable if given a graph in the class, any graph obtained by adding an edge between two connected components of is also in the class. The author…
On tessellations of random maps and the -recurrence
Guillaume Chapuy
We study the masses of the two cells in a Voronoï tessellation of the Brownian surface of genus centered on two uniform random points. Making use of classical bijections…
Laplacian matrices and spanning trees of tree graphs
Philippe Biane, Guillaume Chapuy
If is a strongly connected finite directed graph, the set of rooted directed spanning trees of is naturally equipped with a structure of directed graph: ther…
Connectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture
Guillaume Chapuy, Guillem Perarnau
A class of graphs is bridge-addable if given a graph in the class, any graph obtained by adding an edge between two connected components of is also in the class. We prove a…
Dimers on Rail Yard Graphs
Cédric Boutillier, Jérémie Bouttier, Guillaume Chapuy +2
We introduce a general model of dimer coverings of certain plane bipartite graphs, which we call rail yard graphs (RYG). The transfer matrices used to compute the partition functio…