Programme at the Isaac Newton Institute

Stochastic systems for anomalous diffusion (1 July 2024 to 18 December 2024)

The programme will bring together researchers in probability, stochastic analysis, and related areas, as well as (through applications of anomalous diffusion) mathematical physicists, ecologists, and materials scientists, and (through sampling algorithms) researchers in computational statistics and machine learning. The programme is be built around thematically linked workshops, and will be supported by seminar series, problem sessions, engagement events, and a social programme.

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

• Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness, with Thomas Dreyfus and Andrew Elvey Price (arXiv)
• On the limit law of the superdiffusive elephant random walk, with Hélène Guérin, Lucile Laulin and Thomas Simon (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)

Articles

• Invariant measure of gaps in degenerate competing three-particle systems, with Sandro Franceschi, Tomoyuki Ichiba and Ioannis Karatzas (arXiv)
  Annales de l'Institut Henri Poincaré (to appear)
• A fixed-point equation approach for the superdiffusive elephant random walk, with Hélène Guérin and Lucile Laulin (arXiv)
  Annales de l'Institut Henri Poincaré (to appear)
• Differential transcendence of Bell numbers and relatives: a Galois theoretic approach, with Alin Bostan and Lucia Di Vizio (arXiv)
  American Journal of Mathematics (to appear)
• Logarithmic terms in discrete heat kernel expansions in the quadrant, with Andrew Elvey Price and Andreas Nessmann (arXiv)
  Annales de l'Institut Henri Poincaré D (to appear)
• Elephant polynomials, with Hélène Guérin and Lucile Laulin (arXiv)
  Aequationes mathematicae (to appear)
• Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent, with Luc Hillairet and Helen Jenne (arXiv)
  Annales de l'Institut Henri Poincaré D 11 (2024) 683–713
• Random walks in the high-dimensional limit II: the crinkled subordinator, with Zakhar Kabluchko and Oleksandr Marynych (arXiv)
  Stochastic Processes and their Applications 176 (2024) 104428
• Reflected random walks and unstable Martin boundary, with Irina Ignatiouk-Robert and Irina Kurkova (arXiv)
  Annales de l'Institut Henri Poincaré 60 (2024) 549-587
• 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) 973-988
• 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
• 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, Markov Processes and Related Fields and Queueing Systems: Theory and Applications

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, Hélène Guérin, Charlotte Hardouin, Luc Hillairet, Viet Hung Hoang, Irina Ignatiouk-Robert, Alexander Iksanov, Helen Jenne, Zakhar Kabluchko, Irina Kurkova, Pauline Lafitte-Godillon, Lucile Laulin, Cédric Lecouvey, Johan van Leeuwaarden, Alexander Marynych, Steve Melczer, Marni Mishna, Andreas Nessmann, 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.

Conférences passées

                               



Branching and Persistence (Angers, March 2022, 14-16)