Elliptic Combinatorics: Solving famous models from combinatorics, probability and statistical mechanics, via a transversal approach of special functions

Project Information

COMBINEPIC

Grant agreement ID: 759702

DOI 10.3030/759702

Project closed

EC signature date 19 October 2017

Start date 1 February 2018

End date 31 January 2024

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 242 400,00

EU contribution € 1 242 400,00

Coordinated by

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France

Deliverables

Open Research Data Pilot (3)

Version 3 of the Data Management Plan

Review of the second version of the Data Management Plan as the project will be ending and the data management strategy might have been refined This update deals especially with the data which will be generated after the project completion

Data Management Plan

The Data Management Plan describes the life cycle of the data which will be generated by the project during and after the project completion It will contain information on the types of data that will be generated data and metadata standards policies for data access and sharing data storages and preservation of access

Version 2 of the Data Management Plan

Review of the first version of the Data Management Plan as the project will be developping and the data management strategy might have been refined

Publications

Peer reviewed articles (33)

Boundary behaviour of $$\lambda $$-polyharmonic functions on regular trees

Author(s): Ecaterina Sava-Huss, Wolfgang Woess
Published in: Annali di Matematica Pura ed Applicata (1923 -), 2020, ISSN 0373-3114
Publisher: Nicola Zanichelli
DOI: 10.1007/s10231-020-00981-8

Random walks with drift inside a pyramid: convergence rate for the survival probability

Author(s): Rodolphe Garbit; Kilian Raschel
Published in: ALEA. Latin American Journal of Probability and Mathematical Statistics, Issue 20, 2023, Page(s) 973-988, ISSN 1980-0436
Publisher: Instituto Nacional de Matematica Pura e Aplicada
DOI: 10.30757/alea.v20-35

The six-vertex model on random planar maps revisited

Author(s): Andrew Elvey Price, Paul Zinn-Justin
Published in: Journal of Combinatorial Theory, Series A, Issue 196, 2023, Page(s) 105739, ISSN 0097-3165
Publisher: Academic Press
DOI: 10.1016/j.jcta.2023.105739

Bijections between walks inside a triangular domain and Motzkin paths of bounded amplitude

Author(s): Julien Courtiel, Andrew Elvey Price, Irène Marcovici
Published in: Electronic Journal of Combinatorics, Issue 10778926, 2020, Page(s) Paper No. 2.6, 44, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/9724

Limit shapes for skew Howe duality

Author(s): Betea, Dan; Nazarov, Anton; Scrimshaw, Travis
Published in: Séminaire Lotharingien de Combinatoire, Issue 89B, 2023, Page(s) Paper No. 35, ISSN 1286-4889
Publisher: Univ. Wien, Fak. Math.
DOI: 10.48550/arxiv.2211.13728

Asymptotics of arithmetic functions of GCD and LCM of random integers in hyperbolic regions

Author(s): Alexander Iksanov; Alexander Marynych; Kilian Raschel
Published in: Results in Mathematics, Issue 14226383, 2022, Page(s) Paper No. 165, 22, ISSN 1422-6383
Publisher: Springer Verlag
DOI: 10.1007/s00025-022-01681-w

Phylogenetic trees, augmented perfect matchings and a Thron-type continued fraction (T-fraction) for the Ward polynomials

Author(s): Andrew Elvey Price, Alan D. Sokal
Published in: Electronic Journal of Combinatorics, Issue 10778926, 2020, Page(s) Paper No. 4.6, 36, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/9571

Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks

Author(s): Dreyfus, Thomas; Raschel, Kilian
Published in: Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, Issue 1, 2019, Page(s) 41-80, ISSN 1958-7236
Publisher: Presses universitaires de Franche-Comté
DOI: 10.5802/pmb.29

Recurrence of 2-dimensional queueing processes, and random walk exit times from the quadrant

Author(s): Peigné, Marc; Woess, Wolfgang
Published in: The Annals of Applied Probability, Issue 10505164, 2019, Page(s) 2519--2537, ISSN 1050-5164
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-aap1654

Discrete harmonic functions for non-symmetric Laplace operators in the quarter plane

Author(s): Hoang, Viet Hung
Published in: Markov Processes and Related Fields, Issue 28, 2022, Page(s) 605-653, ISSN 1024-2953
Publisher: Polymat
DOI: 10.48550/arxiv.2201.09985

Boundary behavior of random walks in cones

Author(s): Raschel, Kilian; Tarrago, Pierre
Published in: Markov Processes and Related Fields, Issue 26/4, 2020, Page(s) 711-756, ISSN 1024-2953
Publisher: Polymat

Stieltjes moment sequences for pattern-avoiding permutations

Author(s): Elvey-Price, Andrew; Bostan, Alin; Guttmann, Anthony,; Maillard, Jean-Marie
Published in: Electronic Journal of Combinatorics, Issue 10778926, 2020, Page(s) Paper No. 4.20, 59, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/9402

"Stationary Brownian motion in a <mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML"" display=""inline"" id=""d1e861"" altimg=""si303.svg""><mml:mrow><mml:mn>3</mml:mn><mml:mo>/</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math>-plane: Reduction to a Riemann–Hilbert problem via Fourier transforms"

Author(s): Guy Fayolle; Sandro Franceschi; Kilian Raschel
Published in: Indagationes Mathematicae, Issue 8, 2023, Page(s) 874-890, ISSN 0019-3577
Publisher: Elsevier BV
DOI: 10.1016/j.indag.2022.10.008

Constructing discrete harmonic functions in wedges

Author(s): Hoang, Viet Hung; Raschel, Kilian; Tarrago, Pierre
Published in: Transactions of the American Mathematical Society, Issue 00029947, 2022, Page(s) 4741-4782, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8615

Plane bipolar orientations and quadrant walks

Author(s): Bousquet-Mélou, Mireille; Fusy, Éric; Raschel, Kilian
Published in: Séminaire Lotharingien de Combinatoire, Issue 81, 2020, ISSN 1286-4889
Publisher: Univ. Louis Pasteur Univ. Wien, Fak. Math.

Multivariate Multiplicative Functions of Uniform Random Vectors in Large Integer Domains

Author(s): Zakhar Kabluchko; Alexander Marynych; Kilian Raschel
Published in: Results in Mathematics, Issue 78, 2023, Page(s) Paper No. 201, 22 pp., ISSN 1422-6383
Publisher: Springer Verlag
DOI: 10.1007/s00025-023-01978-4

Martin boundary of random walks in convex cones

Author(s): Duraj, Jetlir; Raschel, Kilian; Tarrago, Pierre; Wachtel, Vitali
Published in: Annales Henri Lebesgue, Issue 26449463, 2020, Page(s) 559-609, ISSN 2644-9463
Publisher: Univ. Rennes 1, ENS Rennes, Ann. H. Lebesgue
DOI: 10.5802/ahl.130

Green's functions with oblique Neumann boundary conditions in a wedge

Author(s): Franceschi, Sandro
Published in: Journal of Theoretical Probability, Issue 08949840, 2019, Page(s) 1775-1810, ISSN 0894-9840
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10959-020-01043-8

On the stationary distribution of reflected Brownian motion in a non-convex wedge

Author(s): Fayolle, Guy; Franceschi, Sandro; Raschel, Kilian
Published in: Markov Processes and Related Fields, Issue 28, 2022, Page(s) 737-772, ISSN 1024-2953
Publisher: Polymat
DOI: 10.48550/arxiv.2102.11754

3D positive lattice walks and spherical triangles

Author(s): B. Bogosel, V. Perrollaz, K. Raschel, A. Trotignon
Published in: Journal of Combinatorial Theory, Series A, Issue 172, 2020, Page(s) 105189, ISSN 0097-3165
Publisher: Academic Press
DOI: 10.1016/j.jcta.2019.105189

The asymptotics of reflectable weighted walks in arbitrary dimension

Author(s): Marni Mishna, Samuel Simon
Published in: Advances in Applied Mathematics, Issue 118, 2020, Page(s) 102043, ISSN 0196-8858
Publisher: Academic Press
DOI: 10.1016/j.aam.2020.102043

Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials

Author(s): Gerold Alsmeyer; Alin Bostan; Kilian Raschel; Thomas Simon
Published in: Advances in Applied Mathematics, Issue 150, 2023, Page(s) Paper No. 102555, 52, ISSN 0196-8858
Publisher: Academic Press
DOI: 10.1016/j.aam.2023.102555

On the least common multiple of several random integers

Author(s): Alin Bostan, Alexander Marynych, Kilian Raschel
Published in: Journal of Number Theory, Issue 204, 2019, Page(s) 113-133, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2019.03.017

The extinction problem for a distylous plant population with sporophytic self-incompatibility

Author(s): Gerold Alsmeyer, Kilian Raschel
Published in: Journal of Mathematical Biology, Issue 78/6, 2019, Page(s) 1841-1874, ISSN 0303-6812
Publisher: Springer Verlag
DOI: 10.1007/s00285-019-01328-5

The Z-invariant Ising model via dimers

Author(s): Cédric Boutillier, Béatrice de Tilière, Kilian Raschel
Published in: Probability Theory and Related Fields, Issue 174/1-2, 2019, Page(s) 235-305, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-018-0861-x

On Walks Avoiding a Quadrant

Author(s): Kilian Raschel, Amélie Trotignon
Published in: The Electronic Journal of Combinatorics, Issue 26/3, 2019, Page(s) 1-34, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/8019

Harmonic functions for singular quadrant walks

Author(s): Viet Hung Hoang; Kilian Raschel; Pierre Tarrago
Published in: Indagationes Mathematicae, Issue 34, 2023, Page(s) 936-972, ISSN 0019-3577
Publisher: Elsevier BV
DOI: 10.1016/j.indag.2023.06.002

A dual skew symmetry for transient reflected Brownian motion in an orthant

Author(s): Sandro Franceschi; Kilian Raschel
Published in: Queueing Systems. Theory and Applications, Issue 102, 2022, ISSN 0257-0130
Publisher: Baltzer Science Publishers B.V.
DOI: 10.1007/s11134-022-09853-9

Asymptotics of 3-Stack-Sortable Permutations

Author(s): Colin Defant; Andrew Elvey Price; Anthony J. Guttmann
Published in: Electronic Journal of Combinatorics, Issue 10778926, 2021, Page(s) Paper No. 2.49, 29, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/10134

Compacted binary trees admit a stretched exponential

Author(s): Andrew Elvey Price, Wenjie Fang, Michael Wallner
Published in: Journal of Combinatorial Theory, Series A, Issue 177, 2021, Page(s) 105306, ISSN 0097-3165
Publisher: Academic Press
DOI: 10.1016/j.jcta.2020.105306

Counting quadrant walks via Tutte's invariant method

Author(s): Olivier Bernardi; Bousquet-Mélou, M.; Raschel, K.
Published in: Combinatorial Theory, Issue 27661334, 2021, Page(s) Paper No. 3, 77, ISSN 2766-1334
Publisher: escholarship.org
DOI: 10.48550/arxiv.1708.08215

On the nature of four models of symmetric walks avoiding a quadrant

Author(s): Dreyfus, Thomas; Trotignon, Amélie
Published in: Annals of Combinatorics, Issue 02180006, 2020, Page(s) pages 617–644, ISSN 0218-0006
Publisher: Springer Verlag
DOI: 10.1007/s00026-021-00541-8

Martin boundary of killed random walks on isoradial graphs

Author(s): Boutillier, Cédric; Raschel, Kilian; Bostan, Alin
Published in: Potential Analysis, Issue 09262601, 2019, Page(s) 201-226, ISSN 0926-2601
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11118-021-09912-5

Other (17)

Reflected random walks and unstable Martin boundary

Author(s): Ignatiouk-Robert, Irina; Kourkova, Irina; Raschel, Kilian
Published in: Preprint, 2020
Publisher: arXiv
DOI: 10.48550/arxiv.2009.11596

Multicritical Schur measures and higher-order analogues of the Tracy-Widom distribution

Author(s): Betea, Dan; Bouttier, Jérémie; Walsh, Harriet
Published in: Preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2307.05303

Elephant polynomials

Author(s): Hélène Guérin, Lucile Laulin, Kilian Raschel
Published in: Preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2401.04959

Branching Random Walks on relatively hyperbolic groups

Author(s): Dussaule, Matthieu; Wang, Longmin; Yang, Wenyuan
Published in: Preprint, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2211.07213

A fixed-point equation approach for the superdiffusive elephant random walk

Author(s): Guérin, Hélène; Laulin, Lucile; Raschel, Kilian
Published in: Preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2308.14630

The generating function of the survival probabilities in a cone is not rational

Author(s): Garbit, Rodolphe; Raschel, Kilian
Published in: Preprint, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2111.05027

Interface fluctuations associated with split Fermi seas

Author(s): Harriet Walsh
Published in: Preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2311.02056

Full asymptotic expansion for orbit-summable quadrant walks and discrete polyharmonic functions

Author(s): Nessmann, Andreas
Published in: Preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2307.11539

Differential transcendence of Bell numbers and relatives: a Galois theoretic approach

Author(s): Bostan, Alin; Di Vizio, Lucia; Raschel, Kilian
Published in: Preprint, 2020
Publisher: arXiv
DOI: 10.48550/arxiv.2012.15292

A local limit theorem for convergent random walks on relatively hyperbolic groups

Author(s): Matthieu Dussaule; Marc Peigné; Samuel Tapie
Published in: Preprint, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2202.11339

The stationary distribution of reflected Brownian motion in a wedge: differential properties

Author(s): Bousquet-Mélou, Mireille; Elvey-Price, Andrew; Franceschi, Sandro; Hardouin, Charlotte; Raschel, Kilian
Published in: Preprint, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2101.01562

Permutations sortable by deques and two stacks in parallel share the same growth rate

Author(s): Price, Andrew Elvey
Published in: Preprint, 2019
Publisher: arXiv preprint server

Random Walks in the High-Dimensional Limit II: The Crinkled Subordinator

Author(s): Kabluchko, Zakhar; Marynych, Alexander; Raschel, Kilian
Published in: Preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2306.04747

Logarithmic terms in discrete heat kernel expansions in the quadrant

Author(s): Elvey-Price, Andrew; Nessmann, Andreas; Raschel, Kilian
Published in: Preprint, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2309.15209

Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent

Author(s): Hillairet, Luc; Jenne, Helen; Raschel, Kilian
Published in: Preprint, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2112.03567

Double-dimer condensation and the PT-DT correspondence

Author(s): Jenne, Helen; Webb, Gautam; Young, Benjamin
Published in: Preprint, 2021
Publisher: arxiv
DOI: 10.48550/arxiv.2109.11773

Invariant measure of gaps in degenerate competing three-particle systems

Author(s): Sandro Franceschi, Tomoyuki Ichiba, Ioannis Karatzas, Kilian Raschel
Published in: Preprint, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2401.10734

Book chapters (1)

Marches aléatoires dans un cône et fonctions discrètes harmoniques

Author(s): Raschel, Kilian; Tarrago, Pierre
Published in: Gazette des Mathématiques, Issue 175, 2023, Page(s) 35-48, ISSN 2826-3235
Publisher: Société Mathématique de France
DOI: 10.48550/arxiv.2211.02925

Monographic books (2)

Topics in statistical mechanics

Author(s): Boutillier, Cédric; Raschel, Kilian; de Tilière, Béatrice
Published in: Panoramas et Synthèses, Issue 59, 2023, ISBN 978-2-85629-970-8
Publisher: Société Mathématique de France (SMF)

Transcendence in Algebra, Combinatorics, Geometry and Number Theory

Author(s): Alin Bostan; Kilian Raschel
Published in: Springer Proceedings in Mathematics & Statistics, 2021, ISBN 978-3-030-84303-8
Publisher: Cham: Springer
DOI: 10.1007/978-3-030-84304-5

Conference proceedings (6)

Asymptotics of Minimal Deterministic FiniteAutomata Recognizing a Finite Binary Language

Author(s): Andrew Elvey Price, Wenjie Fang, Michael Wallner
Published in: Proceedings of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis ofAlgorithms (AofA 2020), Issue Leibniz International Proceedings in Informatics (LIPIcs), 2020, Page(s) 1:1–11:13, ISBN 978-3-95977-147-4
Publisher: Schloss Dagstuhl-Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.aofa.2020.11

The combinatorial PT-DT correspondence

Author(s): Jenne, Helen; Webb, Gautam; Young, Benjamin
Published in: Séminaire Lotharingien de Combinatoire, Issue 12864889, 2021, Page(s) Art. 89, 12, ISSN 1286-4889
Publisher: Univ. Louis Pasteur Univ. Wien, Fak. Math.
DOI: 10.48550/arxiv.2012.08484

Polyharmonic Functions in the Quarter Plane

Author(s): Nessmann, Andreas
Published in: Leibniz International Proceedings in Informatics (LIPIcs), Issue 225, 2022, Page(s) Article No. 15, 16 pp., ISBN 978-3-95977-230-3
Publisher: Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern
DOI: 10.48550/arxiv.2212.07258

Polyharmonic functions and random processes in cones

Author(s): Chapon, Francois; Fusy, Eric; Raschel, Kilian
Published in: Proceedings of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis ofAlgorithms (AofA 2020), Issue Leibniz International Proceedings in Informatics (LIPIcs), 2020, Page(s) 9:1-9:19, ISBN 978-3-95977-147-4
Publisher: Schloss Dagstuhl-Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.aofa.2020.9

Counting lattice walks by winding angle

Author(s): Price, Andrew Elvey
Published in: Séminaire Lotharingien de Combinatoire, Issue 84B, Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics, 2020, Page(s) "Article #43, 12 pp.", ISSN 1286-4889
Publisher: Univ. Louis Pasteur Univ. Wien, Fak. Math.

Eulerian orientations and the six-vertex model on planar maps

Author(s): Mireille Bousquet-Mélou, Andrew Elvey Price, Paul Zinn-Justin
Published in: Séminaire Lotharingien de Combinatoire, Issue 82B, Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics, 2020, Page(s) "Article #70, 12 pp.", ISSN 1286-4889
Publisher: Univ. Louis Pasteur Univ. Wien, Fak. Math.