Publications

Édition de livres

Topics in Statistical Mechanics, edited with Cédric Boutillier and Béatrice de Tilière
Panoramas et Synthèses 59 (2023), French Mathematical Society
Transcendence in Algebra, Combinatorics, Geometry and Number Theory, edited with Alin Bostan
Springer Proceedings in Mathematics and Statistics 373 (2021), Springer

Preprints

Random walks in the high-dimensional limit II: the crinkled subordinator, with Zakhar Kabluchko and Oleksandr Marynych (arXiv)
Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent, with Luc Hillairet and Helen Jenne (arXiv)
The stationary distribution of reflected Brownian motion in a wedge: differential properties, with Mireille Bousquet-Mélou, Andrew Elvey Price, Sandro Franceschi and Charlotte Hardouin (arXiv)
Differential transcendence of Bell numbers and relatives: a Galois theoretic approach, with Alin Bostan and Lucia Di Vizio (arXiv)

Articles publiés

Multivariate multiplicative functions of uniform random vectors in large integer domains, with Zakhar Kabluchko and Oleksandr Marynych (arXiv)
Results in Mathematics 78 (2023) Paper No. 201
Random walks with drift inside a pyramid: convergence rate for the survival probability, with Rodolphe Garbit (arXiv)
ALEA, Latin American Journal of Probability and Mathematical Statistics 20 (2023)
Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials, with Gerold Alsmeyer, Alin Bostan and Thomas Simon (arXiv)
Advances in Applied Mathematics 150 (2023) 102555
Marches aléatoires dans un cône et fonctions discrètes harmoniques, with Pierre Tarrago (arXiv)
La Gazette de la Société Mathématique de France 175 (2023) 35-48
Harmonic functions for singular quadrant walks, with Viet Hung Hoang and Pierre Tarrago (arXiv)
Indagationes Mathematicae 34 (2023) 936-972 (Special issue in honour of J. W. Cohen)
Stationary Brownian motion in a 3/4-plane: reduction to a Riemann-Hilbert problem via Fourier transforms, with Guy Fayolle and Sandro Franceschi (arXiv)
Indagationes Mathematicae 34 (2023) 874-890 (Special issue in honour of J. W. Cohen)
On the stationary distribution of reflected Brownian motion in a non-convex wedge, with Guy Fayolle and Sandro Franceschi (arXiv)
Markov Processes and Related Fields 28 (2022) 737-772
Two accompanying GeoGebra animations
Reflected random walks and unstable Martin boundary, with Irina Ignatiouk-Robert and Irina Kurkova (arXiv)
Annales de l'Institut Henri Poincaré (to appear)
A dual skew symmetry for transient reflected Brownian motion in an orthant, with Sandro Franceschi (arXiv)
Queueing Systems 102 (2022) 123-141 Special issue in honour of Masakiyo Miyazawa
The generating function of the survival probabilities in a cone is not rational, with Rodolphe Garbit (arXiv)
Séminaire Lotharingien de Combinatoire 87B (2022) Special issue for the 9th International Conference on Lattice Path Combinatorics and Applications
Asymptotics of arithmetic functions of GCD and LCM of random integers in hyperbolic regions, with Alexander Iksanov and Alexander Marynych (arXiv)
Results in Mathematics 77 (2022) Paper No. 165
Constructing discrete harmonic functions in wedges, with Viet Hung Hoang and Pierre Tarrago (arXiv)
Transactions of the American Mathematical Society 375 (2022) 4741-4782
Martin boundary of random walks in convex cones, with Jetlir Duraj, Pierre Tarrago and Vitali Wachtel (arXiv)
Annales Henri Lebesgue 5 (2022) 559-609
Counting quadrant walks via Tutte's invariant method, with Olivier Bernardi and Mireille Bousquet-Mélou (arXiv)
Combinatorial Theory 1 (2021) Paper No. 3
The main accompanying Maple session is this one. It points to four other sessions, for the calculation of invariants, of decoupling functions, for proving that no such function exists, and solving the algebraic models.
Extended abstract in DMTCS Proceedings of FPSAC 2016 (2016) 203-214 (arXiv)
Martin boundary of killed random walks on isoradial graphs, with Cédric Boutillier and an appendix by Alin Bostan (arXiv)
Potential Analysis 57 (2022) 201-226
Polyharmonic functions and random processes in cones, with François Chapon and Éric Fusy (arXiv)
Extended abstract in DMTCS Proceedings of AofA 2020 (2020) 1-19 no. 9
Plane bipolar orientations and quadrant walks, with Mireille Bousquet-Mélou and Éric Fusy (arXiv)
Séminaire Lotharingien de Combinatoire 81 (2020) Article B81l
Boundary behavior of random walks in cones, with Pierre Tarrago (arXiv)
Markov Processes and Related Fields 26 (2020) 711-756
3D positive lattice walks and spherical triangles, with Beniamin Bogosel, Vincent Perrollaz and Amélie Trotignon (arXiv)
Journal of Combinatorial Theory, Series A 172 (2020)
Integral expression for the stationary distribution of reflected Brownian motion in a wedge, with Sandro Franceschi (arXiv)
Bernoulli Journal 25 4B (2019) 3673-3713
Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks, with Thomas Dreyfus (arXiv)
Publications Mathématiques de Besançon (2019) 41-80
On walks avoiding a quadrant, with Amélie Trotignon (arXiv)
Electronic Journal of Combinatorics 26 (2019) Paper 3.31 1-34
On the least common multiple of several random integers, with Alin Bostan and Alexander Marynych (arXiv)
Journal of Number Theory 204 (2019) 113-133
The Z-invariant Ising model via dimers, with Cédric Boutillier and Béatrice de Tilière (arXiv)
Probability Theory and Related Fields 174 (2019) 235-305
The extinction problem for a class of distylous plant populations, with Gerold Alsmeyer (arXiv)
Journal of Mathematical Biology 78 (2019) 1841-1874
Tutte's invariant approach for Brownian motion reflected in the quadrant, with Sandro Franceschi (arXiv)
ESAIM: Probability and Statistics 21 (2017) 220-234
Extended abstract in DMTCS Proceedings of AofA 2016 (2016) 1-19 no. 9: Analytic approach for reflected Brownian motion in the quadrant, with Sandro Franceschi and Irina Kurkova (arXiv)
Weighted lattice walks and universality classes, with Julien Courtiel, Steve Melczer and Marni Mishna ( article)
Journal of Combinatorial Theory, Series A 152 (2017) 255-302
The Z-invariant massive Laplacian on isoradial graphs, with Cédric Boutillier and Béatrice de Tilière ( article)
Inventiones mathematicae 208 (2017) 109-189
A human proof of Gessel's lattice path conjecture, with Alin Bostan and Irina Kurkova ( article)
Transactions of the American Mathematical Society 369 (2017) 1365-1393
2022 Robbins Prize
t-Martin boundary of killed random walks in the quadrant, with Cédric Lecouvey ( article)
Séminaire de Probabilités XLVIII (2016) 305-323
On the exit time from a cone for random walks with drift, with Rodolphe Garbit ( article)
Revista Matemática Iberoamericana 32 (2016) 511-532
New steps in walks with small steps in the quarter plane, with Irina Kurkova ( article)
Annals of Combinatorics 19 (2015) 461-511
About a possible analytic approach for walks in the quarter plane with arbitrary big jumps, with Guy Fayolle ( article)
Comptes rendus Mathématique 353 (2015) 89-94
On the exit time from a cone for Brownian motion with drift, with Rodolphe Garbit ( article)
Electronic Journal of Probability 19 (2014) 1-27 no. 63
Random walks in the quarter plane, discrete harmonic functions and conformal mappings, with an appendix by Sandro Franceschi ( article)
Stochastic Processes and their Applications 124 (2014) 3147-3178
Non-D-finite excursions in the quarter plane, with Alin Bostan and Bruno Salvy ( article)
Journal of Combinatorial Theory, Series A 121 (2014) 45-63
Some aspects of fluctuations of random walks on R and applications to random walks on R+ with non-elastic reflection at 0, with Rim Essifi and Marc Peigné ( article)
ALEA, Latin American Journal of Probability and Mathematical Statistics 10 (2013) 591-607
Random walks reaching against all odds the other side of the quarter plane, with Johan van Leeuwaarden ( article)
Journal of Applied Probability 50 (2013) 85-102
Passage time of a random walk in the quarter plane for opinions in the voter model, with Irina Kurkova ( article)
Queueing Systems 74 (2013) 219-234
Extinction probabilities for a distylous plant population modeled by an inhomogeneous random walk on the positive quadrant, with Pauline Lafitte-Godillon and Viet Chi Tran ( article)
SIAM Journal on Applied Mathematics 73 (2013) 700-722
The compensation approach for walks with small steps in the quarter plane, with Ivo Adan and Johan van Leeuwaarden ( article)
Combinatorics, Probability and Computing 22 (2013) 161-183
On the functions counting walks with small steps in the quarter plane, with Irina Kurkova ( article)
Publications Mathématiques de l'IHÉS 116 (2012) 69-114
Some exact asymptotics in the counting of walks in the quarter plane, with Guy Fayolle ( article)
DMTCS Proceedings of AofA 2012 (2012) 109-124
Counting walks in a quadrant: a unified approach via boundary value problems ( article)
Journal of the European Mathematical Society 14 (2012) 749-777
Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group, with Guy Fayolle ( article)
Markov Processes and Related Fields 17 (2011) 619-636
Random walks in Z_+^2 with non-zero drift absorbed at the axes, with Irina Kurkova ( article)
Bulletin de la Société Mathématique de France 139 (2011) 341-387
Green functions for killed random walks in the Weyl chamber of Sp(4) ( article)
Annales de l'Institut Henri Poincaré 47 (2011) 1001-1019
Explicit expression for the generating function counting Gessel's walks, with Irina Kurkova ( article)
Advances in Applied Mathematics 47 (2011) 414-433
Green functions and Martin compactification for killed random walks related to SU(3) ( article)
Electronic Communications in Probability 15 (2010) 176-190
On the holonomy or algebraicity of generating functions counting lattice walks in the quarter plane, with Guy Fayolle ( article)
Markov Processes and Related Fields 16 (2010) 485-496

Theses

Habilitation à Diriger des Recherches (2016): Combinatoire elliptique et marches dans des cônes ( Soutenance)
Manuscript
Thèse de Doctorat (2010): Chemins confinés dans un quadrant ( Soutenance)
Prix de thèse Jacques Neveu 2010
Manuscript

Vulgarisation scientifique

03.16: Article La conjecture de Gessel en combinatoire énumérative, actualité scientifique du CNRS
02.16: Café scientifique, Consulat de France, Vancouver
03.15: Article Compter les excursions sur un échiquier dans le magazine Pour la Science
(A. Bostan et K. Raschel, Pour la Science n°449, pp. 40-46, mars 2015)
09.13: Article Walks in the quarter plane: analytic approach and applications dans les proceedings des Journées MAS 2012
ESAIM: Proceedings 44 (2014) 140-149
11.12: Article Chemins confinés dans un quadrant dans le magazine Matapli
10.12: Article Promenades Mathématiques (écrit avec Marc Peigné) dans le magazine Microscoop du CNRS
10.12: Article sur le Laboratoire de Mathématiques et Physique Théorique de Tours dans La Nouvelle République
03.12: Article Promenades sur le quart de plan de Philippe Pajot dans le magazine La Recherche

Varia

03.14: Oberwolfach report à l'occasion du workshop Enumerative Combinatorics (2014) 57-58

Activités éditoriales

Associate editor for Annals of Combinatorics and for Markov Processes and Related Fields

Thématiques de recherche

Random processes in cones

(Asymptotic and exact expressions for) Green functions, discrete harmonic functions, Martin boundary, exit time from cones, conditioned random walks in cones, combinatorics of walks, generating functions counting walks in cones

Dimer models in statistical mechanics

Stochastic models for population dynamics

Exposés et conférences

Recent research stays and conferences

25-29.06.18: Journées de Probabilités 2018, Tours
28.05.18-01.06.18: Algebra, Arithmetic and Combinatorics of Differential and Difference Equations, CIRM
13-19.05.18: Enumerative combinatorics, Oberwolfach
07-11.05.18: Probabilistic Aspects of Harmonic Analysis, Bedlewo
04-05.12.17: Recursive(ly defined) Stochastic Processes, on the occasion of Gerold Alsmeyer's 60th birthday, Münster
06-08.11.17: Brownian motion in cones: algebraic and analytic approaches, Toulouse
26-29.09.17: Modern perspectives of branching in probability, Münster
17-22.09.17: Lattice walks at the Interface of Algebra, Analysis and Combinatorics, Banff
23.05.17: Journée en hommage à Jacques Neveu, Institut Henri Poincaré
14-16.12.16: Conférence Tours à grands pas
12-14.09.16: 77th Séminaire Lotharingien de Combinatoire, Strobl, Austria
         •Talk #1: Random walks in cones: exponential growth
         •Talk #2: Random walks in cones: critical exponents
         •Talk #3: Discrete harmonic functions and random walks
11-29.07.16: Recherche en binôme au CIRM, avec Alin Bostan
20-24.06.16: Conférence finale de MADACA ( Télécharger le poster)
06-10.06.16: SMF 2016, Tours

Recent talks in seminars

06.18: Séminaire de probabilités et statistiques, Nancy
03.18: Séminaire de Mathématiques appliquées, Nantes
02.18: Séminaire de probabilités, Institut Fourier, Grenoble
01.18: Séminaire de probabilités, ENS Lyon
12.17: Journée Math-STIC sur les marches aléatoires, Paris 13
12.17: Séminaire MODAL'X, Paris Nanterre
09.17: Séminaire de probabilités et statistique, Université de Lille
06.17: Séminaire Calcul stochastique, Université de Strasbourg
09.16: Séminaire Philippe Flajolet, IHP
09.16: Séminaire de Combinatoire du LIX, Polytechnique
05.16: Séminaire de Probabilités, Université de Versailles
04.16: Mathematisches Kolloquium, Wien Universität
01.16: PIMS Colloquium, Simon Fraser University

Coauteurs

Ivo Adan, Gerold Alsmeyer, Olivier Bernardi, Beniamin Bogosel, Alin Bostan, Mireille Bousquet-Mélou, Cédric Boutillier, François Chapon, Julien Courtiel, Béatrice de Tilière, Lucia Di Vizio, Thomas Dreyfus, Jetlir Duraj, Andrew Elvey Price, Rim Essifi, Guy Fayolle, Sandro Franceschi, Éric Fusy, Rodolphe Garbit, Charlotte Hardouin, Luc Hillairet, Viet Hung Hoang, Irina Ignatiouk-Robert, Alexander Iksanov, Helen Jenne, Zakhar Kabluchko, Irina Kurkova, Pauline Lafitte-Godillon, Cédric Lecouvey, Johan van Leeuwaarden, Alexander Marynych, Steve Melczer, Marni Mishna, Marc Peigné, Vincent Perrollaz, Bruno Salvy, Thomas Simon, Pierre Tarrago, Viet Chi Tran, Amélie Trotignon, Vitali Wachtel

Enseignement 2018-2019

Cours au master PUF Vietnam, Hô-Chi-Minh-Ville
Interrogations orales au Lycée Descartes à Tours

MADACA (09/2014-12/2016)

Avec Jérémie Guilhot nous avons été responsables du projet région d'initiative académique intitulé MADACA, sur le thème Marches Aléatoires et processus de Dunkl: Approches Combinatoires et Algébriques.