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

Risultati finali

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

Pubblicazioni

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

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

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

Autori: Rodolphe Garbit; Kilian Raschel
Pubblicato in: ALEA. Latin American Journal of Probability and Mathematical Statistics, Numero 20, 2023, Pagina/e 973-988, ISSN 1980-0436
Editore: Instituto Nacional de Matematica Pura e Aplicada
DOI: 10.30757/alea.v20-35

The six-vertex model on random planar maps revisited

Autori: Andrew Elvey Price, Paul Zinn-Justin
Pubblicato in: Journal of Combinatorial Theory, Series A, Numero 196, 2023, Pagina/e 105739, ISSN 0097-3165
Editore: Academic Press
DOI: 10.1016/j.jcta.2023.105739

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

Autori: Julien Courtiel, Andrew Elvey Price, Irène Marcovici
Pubblicato in: Electronic Journal of Combinatorics, Numero 10778926, 2020, Pagina/e Paper No. 2.6, 44, ISSN 1077-8926
Editore: Electronic Journal of Combinatorics
DOI: 10.37236/9724

Limit shapes for skew Howe duality

Autori: Betea, Dan; Nazarov, Anton; Scrimshaw, Travis
Pubblicato in: Séminaire Lotharingien de Combinatoire, Numero 89B, 2023, Pagina/e Paper No. 35, ISSN 1286-4889
Editore: Univ. Wien, Fak. Math.
DOI: 10.48550/arxiv.2211.13728

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

Autori: Alexander Iksanov; Alexander Marynych; Kilian Raschel
Pubblicato in: Results in Mathematics, Numero 14226383, 2022, Pagina/e Paper No. 165, 22, ISSN 1422-6383
Editore: 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

Autori: Andrew Elvey Price, Alan D. Sokal
Pubblicato in: Electronic Journal of Combinatorics, Numero 10778926, 2020, Pagina/e Paper No. 4.6, 36, ISSN 1077-8926
Editore: Electronic Journal of Combinatorics
DOI: 10.37236/9571

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

Autori: Dreyfus, Thomas; Raschel, Kilian
Pubblicato in: Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, Numero 1, 2019, Pagina/e 41-80, ISSN 1958-7236
Editore: Presses universitaires de Franche-Comté
DOI: 10.5802/pmb.29

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

Autori: Peigné, Marc; Woess, Wolfgang
Pubblicato in: The Annals of Applied Probability, Numero 10505164, 2019, Pagina/e 2519--2537, ISSN 1050-5164
Editore: Institute of Mathematical Statistics
DOI: 10.1214/20-aap1654

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

Autori: Hoang, Viet Hung
Pubblicato in: Markov Processes and Related Fields, Numero 28, 2022, Pagina/e 605-653, ISSN 1024-2953
Editore: Polymat
DOI: 10.48550/arxiv.2201.09985

Boundary behavior of random walks in cones

Autori: Raschel, Kilian; Tarrago, Pierre
Pubblicato in: Markov Processes and Related Fields, Numero 26/4, 2020, Pagina/e 711-756, ISSN 1024-2953
Editore: Polymat

Stieltjes moment sequences for pattern-avoiding permutations

Autori: Elvey-Price, Andrew; Bostan, Alin; Guttmann, Anthony,; Maillard, Jean-Marie
Pubblicato in: Electronic Journal of Combinatorics, Numero 10778926, 2020, Pagina/e Paper No. 4.20, 59, ISSN 1077-8926
Editore: 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"

Autori: Guy Fayolle; Sandro Franceschi; Kilian Raschel
Pubblicato in: Indagationes Mathematicae, Numero 8, 2023, Pagina/e 874-890, ISSN 0019-3577
Editore: Elsevier BV
DOI: 10.1016/j.indag.2022.10.008

Constructing discrete harmonic functions in wedges

Autori: Hoang, Viet Hung; Raschel, Kilian; Tarrago, Pierre
Pubblicato in: Transactions of the American Mathematical Society, Numero 00029947, 2022, Pagina/e 4741-4782, ISSN 0002-9947
Editore: American Mathematical Society
DOI: 10.1090/tran/8615

Plane bipolar orientations and quadrant walks

Autori: Bousquet-Mélou, Mireille; Fusy, Éric; Raschel, Kilian
Pubblicato in: Séminaire Lotharingien de Combinatoire, Numero 81, 2020, ISSN 1286-4889
Editore: Univ. Louis Pasteur Univ. Wien, Fak. Math.

Multivariate Multiplicative Functions of Uniform Random Vectors in Large Integer Domains

Autori: Zakhar Kabluchko; Alexander Marynych; Kilian Raschel
Pubblicato in: Results in Mathematics, Numero 78, 2023, Pagina/e Paper No. 201, 22 pp., ISSN 1422-6383
Editore: Springer Verlag
DOI: 10.1007/s00025-023-01978-4

Martin boundary of random walks in convex cones

Autori: Duraj, Jetlir; Raschel, Kilian; Tarrago, Pierre; Wachtel, Vitali
Pubblicato in: Annales Henri Lebesgue, Numero 26449463, 2020, Pagina/e 559-609, ISSN 2644-9463
Editore: Univ. Rennes 1, ENS Rennes, Ann. H. Lebesgue
DOI: 10.5802/ahl.130

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

Autori: Franceschi, Sandro
Pubblicato in: Journal of Theoretical Probability, Numero 08949840, 2019, Pagina/e 1775-1810, ISSN 0894-9840
Editore: Kluwer Academic Publishers
DOI: 10.1007/s10959-020-01043-8

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

Autori: Fayolle, Guy; Franceschi, Sandro; Raschel, Kilian
Pubblicato in: Markov Processes and Related Fields, Numero 28, 2022, Pagina/e 737-772, ISSN 1024-2953
Editore: Polymat
DOI: 10.48550/arxiv.2102.11754

3D positive lattice walks and spherical triangles

Autori: B. Bogosel, V. Perrollaz, K. Raschel, A. Trotignon
Pubblicato in: Journal of Combinatorial Theory, Series A, Numero 172, 2020, Pagina/e 105189, ISSN 0097-3165
Editore: Academic Press
DOI: 10.1016/j.jcta.2019.105189

The asymptotics of reflectable weighted walks in arbitrary dimension

Autori: Marni Mishna, Samuel Simon
Pubblicato in: Advances in Applied Mathematics, Numero 118, 2020, Pagina/e 102043, ISSN 0196-8858
Editore: Academic Press
DOI: 10.1016/j.aam.2020.102043

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

Autori: Gerold Alsmeyer; Alin Bostan; Kilian Raschel; Thomas Simon
Pubblicato in: Advances in Applied Mathematics, Numero 150, 2023, Pagina/e Paper No. 102555, 52, ISSN 0196-8858
Editore: Academic Press
DOI: 10.1016/j.aam.2023.102555

On the least common multiple of several random integers

Autori: Alin Bostan, Alexander Marynych, Kilian Raschel
Pubblicato in: Journal of Number Theory, Numero 204, 2019, Pagina/e 113-133, ISSN 0022-314X
Editore: Academic Press
DOI: 10.1016/j.jnt.2019.03.017

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

Autori: Gerold Alsmeyer, Kilian Raschel
Pubblicato in: Journal of Mathematical Biology, Numero 78/6, 2019, Pagina/e 1841-1874, ISSN 0303-6812
Editore: Springer Verlag
DOI: 10.1007/s00285-019-01328-5

The Z-invariant Ising model via dimers

Autori: Cédric Boutillier, Béatrice de Tilière, Kilian Raschel
Pubblicato in: Probability Theory and Related Fields, Numero 174/1-2, 2019, Pagina/e 235-305, ISSN 0178-8051
Editore: Springer Verlag
DOI: 10.1007/s00440-018-0861-x

On Walks Avoiding a Quadrant

Autori: Kilian Raschel, Amélie Trotignon
Pubblicato in: The Electronic Journal of Combinatorics, Numero 26/3, 2019, Pagina/e 1-34, ISSN 1077-8926
Editore: Electronic Journal of Combinatorics
DOI: 10.37236/8019

Harmonic functions for singular quadrant walks

Autori: Viet Hung Hoang; Kilian Raschel; Pierre Tarrago
Pubblicato in: Indagationes Mathematicae, Numero 34, 2023, Pagina/e 936-972, ISSN 0019-3577
Editore: Elsevier BV
DOI: 10.1016/j.indag.2023.06.002

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

Autori: Sandro Franceschi; Kilian Raschel
Pubblicato in: Queueing Systems. Theory and Applications, Numero 102, 2022, ISSN 0257-0130
Editore: Baltzer Science Publishers B.V.
DOI: 10.1007/s11134-022-09853-9

Asymptotics of 3-Stack-Sortable Permutations

Autori: Colin Defant; Andrew Elvey Price; Anthony J. Guttmann
Pubblicato in: Electronic Journal of Combinatorics, Numero 10778926, 2021, Pagina/e Paper No. 2.49, 29, ISSN 1077-8926
Editore: Electronic Journal of Combinatorics
DOI: 10.37236/10134

Compacted binary trees admit a stretched exponential

Autori: Andrew Elvey Price, Wenjie Fang, Michael Wallner
Pubblicato in: Journal of Combinatorial Theory, Series A, Numero 177, 2021, Pagina/e 105306, ISSN 0097-3165
Editore: Academic Press
DOI: 10.1016/j.jcta.2020.105306

Counting quadrant walks via Tutte's invariant method

Autori: Olivier Bernardi; Bousquet-Mélou, M.; Raschel, K.
Pubblicato in: Combinatorial Theory, Numero 27661334, 2021, Pagina/e Paper No. 3, 77, ISSN 2766-1334
Editore: escholarship.org
DOI: 10.48550/arxiv.1708.08215

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

Autori: Dreyfus, Thomas; Trotignon, Amélie
Pubblicato in: Annals of Combinatorics, Numero 02180006, 2020, Pagina/e pages 617–644, ISSN 0218-0006
Editore: Springer Verlag
DOI: 10.1007/s00026-021-00541-8

Martin boundary of killed random walks on isoradial graphs

Autori: Boutillier, Cédric; Raschel, Kilian; Bostan, Alin
Pubblicato in: Potential Analysis, Numero 09262601, 2019, Pagina/e 201-226, ISSN 0926-2601
Editore: Kluwer Academic Publishers
DOI: 10.1007/s11118-021-09912-5

Reflected random walks and unstable Martin boundary

Autori: Ignatiouk-Robert, Irina; Kourkova, Irina; Raschel, Kilian
Pubblicato in: Preprint, 2020
Editore: arXiv
DOI: 10.48550/arxiv.2009.11596

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

Autori: Betea, Dan; Bouttier, Jérémie; Walsh, Harriet
Pubblicato in: Preprint, 2023
Editore: arXiv
DOI: 10.48550/arxiv.2307.05303

Elephant polynomials

Autori: Hélène Guérin, Lucile Laulin, Kilian Raschel
Pubblicato in: Preprint, 2023
Editore: arXiv
DOI: 10.48550/arxiv.2401.04959

Branching Random Walks on relatively hyperbolic groups

Autori: Dussaule, Matthieu; Wang, Longmin; Yang, Wenyuan
Pubblicato in: Preprint, 2022
Editore: arXiv
DOI: 10.48550/arxiv.2211.07213

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

Autori: Guérin, Hélène; Laulin, Lucile; Raschel, Kilian
Pubblicato in: Preprint, 2023
Editore: arXiv
DOI: 10.48550/arxiv.2308.14630

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

Autori: Garbit, Rodolphe; Raschel, Kilian
Pubblicato in: Preprint, 2021
Editore: arXiv
DOI: 10.48550/arxiv.2111.05027

Interface fluctuations associated with split Fermi seas

Autori: Harriet Walsh
Pubblicato in: Preprint, 2023
Editore: arXiv
DOI: 10.48550/arxiv.2311.02056

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

Autori: Nessmann, Andreas
Pubblicato in: Preprint, 2023
Editore: arXiv
DOI: 10.48550/arxiv.2307.11539

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

Autori: Bostan, Alin; Di Vizio, Lucia; Raschel, Kilian
Pubblicato in: Preprint, 2020
Editore: arXiv
DOI: 10.48550/arxiv.2012.15292

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

Autori: Matthieu Dussaule; Marc Peigné; Samuel Tapie
Pubblicato in: Preprint, 2022
Editore: arXiv
DOI: 10.48550/arxiv.2202.11339

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

Autori: Bousquet-Mélou, Mireille; Elvey-Price, Andrew; Franceschi, Sandro; Hardouin, Charlotte; Raschel, Kilian
Pubblicato in: Preprint, 2021
Editore: arXiv
DOI: 10.48550/arxiv.2101.01562

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

Autori: Price, Andrew Elvey
Pubblicato in: Preprint, 2019
Editore: arXiv preprint server

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

Autori: Kabluchko, Zakhar; Marynych, Alexander; Raschel, Kilian
Pubblicato in: Preprint, 2023
Editore: arXiv
DOI: 10.48550/arxiv.2306.04747

Logarithmic terms in discrete heat kernel expansions in the quadrant

Autori: Elvey-Price, Andrew; Nessmann, Andreas; Raschel, Kilian
Pubblicato in: Preprint, 2023
Editore: arXiv
DOI: 10.48550/arxiv.2309.15209

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

Autori: Hillairet, Luc; Jenne, Helen; Raschel, Kilian
Pubblicato in: Preprint, 2021
Editore: arXiv
DOI: 10.48550/arxiv.2112.03567

Double-dimer condensation and the PT-DT correspondence

Autori: Jenne, Helen; Webb, Gautam; Young, Benjamin
Pubblicato in: Preprint, 2021
Editore: arxiv
DOI: 10.48550/arxiv.2109.11773

Invariant measure of gaps in degenerate competing three-particle systems

Autori: Sandro Franceschi, Tomoyuki Ichiba, Ioannis Karatzas, Kilian Raschel
Pubblicato in: Preprint, 2024
Editore: arXiv
DOI: 10.48550/arxiv.2401.10734

Marches aléatoires dans un cône et fonctions discrètes harmoniques

Autori: Raschel, Kilian; Tarrago, Pierre
Pubblicato in: Gazette des Mathématiques, Numero 175, 2023, Pagina/e 35-48, ISSN 2826-3235
Editore: Société Mathématique de France
DOI: 10.48550/arxiv.2211.02925

Topics in statistical mechanics

Autori: Boutillier, Cédric; Raschel, Kilian; de Tilière, Béatrice
Pubblicato in: Panoramas et Synthèses, Numero 59, 2023, ISBN 978-2-85629-970-8
Editore: Société Mathématique de France (SMF)

Transcendence in Algebra, Combinatorics, Geometry and Number Theory

Autori: Alin Bostan; Kilian Raschel
Pubblicato in: Springer Proceedings in Mathematics & Statistics, 2021, ISBN 978-3-030-84303-8
Editore: Cham: Springer
DOI: 10.1007/978-3-030-84304-5

Asymptotics of Minimal Deterministic FiniteAutomata Recognizing a Finite Binary Language

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

The combinatorial PT-DT correspondence

Autori: Jenne, Helen; Webb, Gautam; Young, Benjamin
Pubblicato in: Séminaire Lotharingien de Combinatoire, Numero 12864889, 2021, Pagina/e Art. 89, 12, ISSN 1286-4889
Editore: Univ. Louis Pasteur Univ. Wien, Fak. Math.
DOI: 10.48550/arxiv.2012.08484

Polyharmonic Functions in the Quarter Plane

Autori: Nessmann, Andreas
Pubblicato in: Leibniz International Proceedings in Informatics (LIPIcs), Numero 225, 2022, Pagina/e Article No. 15, 16 pp., ISBN 978-3-95977-230-3
Editore: Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern
DOI: 10.48550/arxiv.2212.07258

Polyharmonic functions and random processes in cones

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

Counting lattice walks by winding angle

Autori: Price, Andrew Elvey
Pubblicato in: Séminaire Lotharingien de Combinatoire, Numero 84B, Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics, 2020, Pagina/e "Article #43, 12 pp.", ISSN 1286-4889
Editore: Univ. Louis Pasteur Univ. Wien, Fak. Math.

Eulerian orientations and the six-vertex model on planar maps

Autori: Mireille Bousquet-Mélou, Andrew Elvey Price, Paul Zinn-Justin
Pubblicato in: Séminaire Lotharingien de Combinatoire, Numero 82B, Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics, 2020, Pagina/e "Article #70, 12 pp.", ISSN 1286-4889
Editore: Univ. Louis Pasteur Univ. Wien, Fak. Math.

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