Jérémie Bouttier
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View article: Enumeration of maps with tight boundaries and the Zhukovsky transformation
Enumeration of maps with tight boundaries and the Zhukovsky transformation Open
We consider maps with tight boundaries, i.e., maps whose boundaries have minimal length in their homotopy class, and discuss the properties of their generating functions T^{(g)}_{\ell_1,\ldots,\ell_n} for fixed genus g and prescribed bound…
View article: The slice decomposition of planar hypermaps
The slice decomposition of planar hypermaps Open
The slice decomposition is a bijective method for enumerating planar maps (graphs embedded in the sphere) with control over face degrees. In this paper, we extend the slice decomposition to the richer setting of hypermaps, naturally interp…
View article: Enumeration of planar bipartite tight irreducible maps
Enumeration of planar bipartite tight irreducible maps Open
We consider planar bipartite maps which are both tight, i.e. without vertices of degree $1$, and $2b$-irreducible, i.e. such that each cycle has length at least $2b$ and such that any cycle of length exactly $2b$ is the contour of a face. …
View article: On quasi-polynomials counting planar tight maps
On quasi-polynomials counting planar tight maps Open
A tight map is a map with some of its vertices marked, such that every vertex of degree \\(1\\) is marked. We give an explicit formula for the number \\(N_{0,n}(d_1,\\ldots,d_n)\\) of planar tight maps with \\(n\\) labeled faces of prescri…
View article: Multicritical Schur Measures and Higher-Order Analogues of the Tracy–Widom Distribution
Multicritical Schur Measures and Higher-Order Analogues of the Tracy–Widom Distribution Open
View article: Nesting Statistics in the O(n) Loop Model on Random Planar Maps
Nesting Statistics in the O(n) Loop Model on Random Planar Maps Open
View article: Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants
Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants Open
We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively by …
View article: From point processes to quantum optics and back
From point processes to quantum optics and back Open
Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. Her initial motivation was to provide models for the set of detection times in fundamental bosonic or fermionic optical…
View article: From point processes to quantum optics and back
From point processes to quantum optics and back Open
Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced\npermanental and determinantal point processes. Her initial motivation was to\nprovide models for the set of detection times in fundamental bosonic or\nfermionic opti…
View article: On quasi-polynomials counting planar tight maps
On quasi-polynomials counting planar tight maps Open
A tight map is a map with some of its vertices marked, such that every vertex of degree $1$ is marked. We give an explicit formula for the number $N_{0,n}(d_1,\ldots,d_n)$ of planar tight maps with $n$ labeled faces of prescribed degrees $…
View article: Multicritical random partitions
Multicritical random partitions Open
12 pages, 3 figures
View article: Enumeration of Planar Constellations with an Alternating Boundary
Enumeration of Planar Constellations with an Alternating Boundary Open
A planar hypermap with a boundary is defined as a planar map with a boundary, endowed with a proper bicoloring of the inner faces. The boundary is said alternating if the colors of the incident inner faces alternate along its contour. In t…
View article: Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants
Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants Open
We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively by …
View article: Multicritical random partitions
Multicritical random partitions Open
We study two families of probability measures on integer partitions, which are Schur measures with parameters tuned in such a way that the edge fluctuations are characterized by a critical exponent different from the generic $1/3$. We find…
View article: Planar maps and random partitions
Planar maps and random partitions Open
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general map-mobi…
View article: New edge asymptotics of skew Young diagrams via free boundaries
New edge asymptotics of skew Young diagrams via free boundaries Open
We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's pro…
View article: The Periodic Schur Process and Free Fermions at Finite Temperature
The Periodic Schur Process and Free Fermions at Finite Temperature Open
View article: Autour de la mesure de Plancherel sur les partitions d'entiers (une introduction aux processus de Schur) - Partie 2
Autour de la mesure de Plancherel sur les partitions d'entiers (une introduction aux processus de Schur) - Partie 2 Open
Le but de ce cours sera de présenter quelques techniques liées aux processus de Schur, dans le cadre le plus simple de la mesure de Plancherel sur les partitions d'entiers. La mesure de Plancherel est une mesure sur l'ensemble des partitio…
View article: The Free Boundary Schur Process and Applications I
The Free Boundary Schur Process and Applications I Open
View article: Bumping sequences and multispecies juggling
Bumping sequences and multispecies juggling Open
View article: The free boundary Schur process and applications
The free boundary Schur process and applications Open
75 pages, 21 figures. This document is the full article with all proofs. An extended abstract was presented at FPSAC 2017, see hal-01510975.
View article: Nesting statistics in the O(n) loop model on random planar maps
Nesting statistics in the O(n) loop model on random planar maps Open
In the O(n) loop model on random planar maps, we study the depth - in terms of the number of levels of nesting - of the loop configuration, by means of analytic combinatorics. We focus on the 'refined' generating series of pointed disks or…
View article: Some generalized juggling processes
Some generalized juggling processes Open
We consider generalizations of juggling Markov chains introduced by Ayyer, Bouttier, Corteel and Nunzi. We first study multispecies generalizations of all the finite models therein, namely the MJMC, the add-drop and the annihilation models…
View article: Multivariate juggling probabilities
Multivariate juggling probabilities Open
We consider refined versions of Markov chains related to juggling introduced\nby Warrington. We further generalize the construction to juggling with\narbitrary heights as well as infinitely many balls, which are expressed more\nsuccinctly …
View article: Some generalized juggling processes (extended abstract)
Some generalized juggling processes (extended abstract) Open
We consider generalizations of juggling Markov chains introduced by Ayyer, Bouttier, Corteel and Nunzi. We first study multispecies generalizations of all the finite models therein, namely the MJMC, the add-drop and the annihilation models…