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

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

Autores: Ecaterina Sava-Huss, Wolfgang Woess
Publicado en: Annali di Matematica Pura ed Applicata (1923 -), 2020, ISSN 0373-3114
Editor: Nicola Zanichelli
DOI: 10.1007/s10231-020-00981-8

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

Autores: Rodolphe Garbit; Kilian Raschel
Publicado en: ALEA. Latin American Journal of Probability and Mathematical Statistics, Edición 20, 2023, Página(s) 973-988, ISSN 1980-0436
Editor: Instituto Nacional de Matematica Pura e Aplicada
DOI: 10.30757/alea.v20-35

The six-vertex model on random planar maps revisited

Autores: Andrew Elvey Price, Paul Zinn-Justin
Publicado en: Journal of Combinatorial Theory, Series A, Edición 196, 2023, Página(s) 105739, ISSN 0097-3165
Editor: Academic Press
DOI: 10.1016/j.jcta.2023.105739

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

Autores: Julien Courtiel, Andrew Elvey Price, Irène Marcovici
Publicado en: Electronic Journal of Combinatorics, Edición 10778926, 2020, Página(s) Paper No. 2.6, 44, ISSN 1077-8926
Editor: Electronic Journal of Combinatorics
DOI: 10.37236/9724

Limit shapes for skew Howe duality

Autores: Betea, Dan; Nazarov, Anton; Scrimshaw, Travis
Publicado en: Séminaire Lotharingien de Combinatoire, Edición 89B, 2023, Página(s) Paper No. 35, ISSN 1286-4889
Editor: Univ. Wien, Fak. Math.
DOI: 10.48550/arxiv.2211.13728

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

Autores: Alexander Iksanov; Alexander Marynych; Kilian Raschel
Publicado en: Results in Mathematics, Edición 14226383, 2022, Página(s) Paper No. 165, 22, ISSN 1422-6383
Editor: 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

Autores: Andrew Elvey Price, Alan D. Sokal
Publicado en: Electronic Journal of Combinatorics, Edición 10778926, 2020, Página(s) Paper No. 4.6, 36, ISSN 1077-8926
Editor: Electronic Journal of Combinatorics
DOI: 10.37236/9571

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

Autores: Dreyfus, Thomas; Raschel, Kilian
Publicado en: Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, Edición 1, 2019, Página(s) 41-80, ISSN 1958-7236
Editor: Presses universitaires de Franche-Comté
DOI: 10.5802/pmb.29

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

Autores: Peigné, Marc; Woess, Wolfgang
Publicado en: The Annals of Applied Probability, Edición 10505164, 2019, Página(s) 2519--2537, ISSN 1050-5164
Editor: Institute of Mathematical Statistics
DOI: 10.1214/20-aap1654

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

Autores: Hoang, Viet Hung
Publicado en: Markov Processes and Related Fields, Edición 28, 2022, Página(s) 605-653, ISSN 1024-2953
Editor: Polymat
DOI: 10.48550/arxiv.2201.09985

Boundary behavior of random walks in cones

Autores: Raschel, Kilian; Tarrago, Pierre
Publicado en: Markov Processes and Related Fields, Edición 26/4, 2020, Página(s) 711-756, ISSN 1024-2953
Editor: Polymat

Stieltjes moment sequences for pattern-avoiding permutations

Autores: Elvey-Price, Andrew; Bostan, Alin; Guttmann, Anthony,; Maillard, Jean-Marie
Publicado en: Electronic Journal of Combinatorics, Edición 10778926, 2020, Página(s) Paper No. 4.20, 59, ISSN 1077-8926
Editor: 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"

Autores: Guy Fayolle; Sandro Franceschi; Kilian Raschel
Publicado en: Indagationes Mathematicae, Edición 8, 2023, Página(s) 874-890, ISSN 0019-3577
Editor: Elsevier BV
DOI: 10.1016/j.indag.2022.10.008

Constructing discrete harmonic functions in wedges

Autores: Hoang, Viet Hung; Raschel, Kilian; Tarrago, Pierre
Publicado en: Transactions of the American Mathematical Society, Edición 00029947, 2022, Página(s) 4741-4782, ISSN 0002-9947
Editor: American Mathematical Society
DOI: 10.1090/tran/8615

Plane bipolar orientations and quadrant walks

Autores: Bousquet-Mélou, Mireille; Fusy, Éric; Raschel, Kilian
Publicado en: Séminaire Lotharingien de Combinatoire, Edición 81, 2020, ISSN 1286-4889
Editor: Univ. Louis Pasteur Univ. Wien, Fak. Math.

Multivariate Multiplicative Functions of Uniform Random Vectors in Large Integer Domains

Autores: Zakhar Kabluchko; Alexander Marynych; Kilian Raschel
Publicado en: Results in Mathematics, Edición 78, 2023, Página(s) Paper No. 201, 22 pp., ISSN 1422-6383
Editor: Springer Verlag
DOI: 10.1007/s00025-023-01978-4

Martin boundary of random walks in convex cones

Autores: Duraj, Jetlir; Raschel, Kilian; Tarrago, Pierre; Wachtel, Vitali
Publicado en: Annales Henri Lebesgue, Edición 26449463, 2020, Página(s) 559-609, ISSN 2644-9463
Editor: Univ. Rennes 1, ENS Rennes, Ann. H. Lebesgue
DOI: 10.5802/ahl.130

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

Autores: Franceschi, Sandro
Publicado en: Journal of Theoretical Probability, Edición 08949840, 2019, Página(s) 1775-1810, ISSN 0894-9840
Editor: Kluwer Academic Publishers
DOI: 10.1007/s10959-020-01043-8

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

Autores: Fayolle, Guy; Franceschi, Sandro; Raschel, Kilian
Publicado en: Markov Processes and Related Fields, Edición 28, 2022, Página(s) 737-772, ISSN 1024-2953
Editor: Polymat
DOI: 10.48550/arxiv.2102.11754

3D positive lattice walks and spherical triangles

Autores: B. Bogosel, V. Perrollaz, K. Raschel, A. Trotignon
Publicado en: Journal of Combinatorial Theory, Series A, Edición 172, 2020, Página(s) 105189, ISSN 0097-3165
Editor: Academic Press
DOI: 10.1016/j.jcta.2019.105189

The asymptotics of reflectable weighted walks in arbitrary dimension

Autores: Marni Mishna, Samuel Simon
Publicado en: Advances in Applied Mathematics, Edición 118, 2020, Página(s) 102043, ISSN 0196-8858
Editor: Academic Press
DOI: 10.1016/j.aam.2020.102043

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

Autores: Gerold Alsmeyer; Alin Bostan; Kilian Raschel; Thomas Simon
Publicado en: Advances in Applied Mathematics, Edición 150, 2023, Página(s) Paper No. 102555, 52, ISSN 0196-8858
Editor: Academic Press
DOI: 10.1016/j.aam.2023.102555

On the least common multiple of several random integers

Autores: Alin Bostan, Alexander Marynych, Kilian Raschel
Publicado en: Journal of Number Theory, Edición 204, 2019, Página(s) 113-133, ISSN 0022-314X
Editor: Academic Press
DOI: 10.1016/j.jnt.2019.03.017

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

Autores: Gerold Alsmeyer, Kilian Raschel
Publicado en: Journal of Mathematical Biology, Edición 78/6, 2019, Página(s) 1841-1874, ISSN 0303-6812
Editor: Springer Verlag
DOI: 10.1007/s00285-019-01328-5

The Z-invariant Ising model via dimers

Autores: Cédric Boutillier, Béatrice de Tilière, Kilian Raschel
Publicado en: Probability Theory and Related Fields, Edición 174/1-2, 2019, Página(s) 235-305, ISSN 0178-8051
Editor: Springer Verlag
DOI: 10.1007/s00440-018-0861-x

On Walks Avoiding a Quadrant

Autores: Kilian Raschel, Amélie Trotignon
Publicado en: The Electronic Journal of Combinatorics, Edición 26/3, 2019, Página(s) 1-34, ISSN 1077-8926
Editor: Electronic Journal of Combinatorics
DOI: 10.37236/8019

Harmonic functions for singular quadrant walks

Autores: Viet Hung Hoang; Kilian Raschel; Pierre Tarrago
Publicado en: Indagationes Mathematicae, Edición 34, 2023, Página(s) 936-972, ISSN 0019-3577
Editor: Elsevier BV
DOI: 10.1016/j.indag.2023.06.002

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

Autores: Sandro Franceschi; Kilian Raschel
Publicado en: Queueing Systems. Theory and Applications, Edición 102, 2022, ISSN 0257-0130
Editor: Baltzer Science Publishers B.V.
DOI: 10.1007/s11134-022-09853-9

Asymptotics of 3-Stack-Sortable Permutations

Autores: Colin Defant; Andrew Elvey Price; Anthony J. Guttmann
Publicado en: Electronic Journal of Combinatorics, Edición 10778926, 2021, Página(s) Paper No. 2.49, 29, ISSN 1077-8926
Editor: Electronic Journal of Combinatorics
DOI: 10.37236/10134

Compacted binary trees admit a stretched exponential

Autores: Andrew Elvey Price, Wenjie Fang, Michael Wallner
Publicado en: Journal of Combinatorial Theory, Series A, Edición 177, 2021, Página(s) 105306, ISSN 0097-3165
Editor: Academic Press
DOI: 10.1016/j.jcta.2020.105306

Counting quadrant walks via Tutte's invariant method

Autores: Olivier Bernardi; Bousquet-Mélou, M.; Raschel, K.
Publicado en: Combinatorial Theory, Edición 27661334, 2021, Página(s) Paper No. 3, 77, ISSN 2766-1334
Editor: escholarship.org
DOI: 10.48550/arxiv.1708.08215

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

Autores: Dreyfus, Thomas; Trotignon, Amélie
Publicado en: Annals of Combinatorics, Edición 02180006, 2020, Página(s) pages 617–644, ISSN 0218-0006
Editor: Springer Verlag
DOI: 10.1007/s00026-021-00541-8

Martin boundary of killed random walks on isoradial graphs

Autores: Boutillier, Cédric; Raschel, Kilian; Bostan, Alin
Publicado en: Potential Analysis, Edición 09262601, 2019, Página(s) 201-226, ISSN 0926-2601
Editor: Kluwer Academic Publishers
DOI: 10.1007/s11118-021-09912-5

Reflected random walks and unstable Martin boundary

Autores: Ignatiouk-Robert, Irina; Kourkova, Irina; Raschel, Kilian
Publicado en: Preprint, 2020
Editor: arXiv
DOI: 10.48550/arxiv.2009.11596

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

Autores: Betea, Dan; Bouttier, Jérémie; Walsh, Harriet
Publicado en: Preprint, 2023
Editor: arXiv
DOI: 10.48550/arxiv.2307.05303

Elephant polynomials

Autores: Hélène Guérin, Lucile Laulin, Kilian Raschel
Publicado en: Preprint, 2023
Editor: arXiv
DOI: 10.48550/arxiv.2401.04959

Branching Random Walks on relatively hyperbolic groups

Autores: Dussaule, Matthieu; Wang, Longmin; Yang, Wenyuan
Publicado en: Preprint, 2022
Editor: arXiv
DOI: 10.48550/arxiv.2211.07213

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

Autores: Guérin, Hélène; Laulin, Lucile; Raschel, Kilian
Publicado en: Preprint, 2023
Editor: arXiv
DOI: 10.48550/arxiv.2308.14630

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

Autores: Garbit, Rodolphe; Raschel, Kilian
Publicado en: Preprint, 2021
Editor: arXiv
DOI: 10.48550/arxiv.2111.05027

Interface fluctuations associated with split Fermi seas

Autores: Harriet Walsh
Publicado en: Preprint, 2023
Editor: arXiv
DOI: 10.48550/arxiv.2311.02056

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

Autores: Nessmann, Andreas
Publicado en: Preprint, 2023
Editor: arXiv
DOI: 10.48550/arxiv.2307.11539

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

Autores: Bostan, Alin; Di Vizio, Lucia; Raschel, Kilian
Publicado en: Preprint, 2020
Editor: arXiv
DOI: 10.48550/arxiv.2012.15292

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

Autores: Matthieu Dussaule; Marc Peigné; Samuel Tapie
Publicado en: Preprint, 2022
Editor: arXiv
DOI: 10.48550/arxiv.2202.11339

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

Autores: Bousquet-Mélou, Mireille; Elvey-Price, Andrew; Franceschi, Sandro; Hardouin, Charlotte; Raschel, Kilian
Publicado en: Preprint, 2021
Editor: arXiv
DOI: 10.48550/arxiv.2101.01562

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

Autores: Price, Andrew Elvey
Publicado en: Preprint, 2019
Editor: arXiv preprint server

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

Autores: Kabluchko, Zakhar; Marynych, Alexander; Raschel, Kilian
Publicado en: Preprint, 2023
Editor: arXiv
DOI: 10.48550/arxiv.2306.04747

Logarithmic terms in discrete heat kernel expansions in the quadrant

Autores: Elvey-Price, Andrew; Nessmann, Andreas; Raschel, Kilian
Publicado en: Preprint, 2023
Editor: arXiv
DOI: 10.48550/arxiv.2309.15209

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

Autores: Hillairet, Luc; Jenne, Helen; Raschel, Kilian
Publicado en: Preprint, 2021
Editor: arXiv
DOI: 10.48550/arxiv.2112.03567

Double-dimer condensation and the PT-DT correspondence

Autores: Jenne, Helen; Webb, Gautam; Young, Benjamin
Publicado en: Preprint, 2021
Editor: arxiv
DOI: 10.48550/arxiv.2109.11773

Invariant measure of gaps in degenerate competing three-particle systems

Autores: Sandro Franceschi, Tomoyuki Ichiba, Ioannis Karatzas, Kilian Raschel
Publicado en: Preprint, 2024
Editor: arXiv
DOI: 10.48550/arxiv.2401.10734

Marches aléatoires dans un cône et fonctions discrètes harmoniques

Autores: Raschel, Kilian; Tarrago, Pierre
Publicado en: Gazette des Mathématiques, Edición 175, 2023, Página(s) 35-48, ISSN 2826-3235
Editor: Société Mathématique de France
DOI: 10.48550/arxiv.2211.02925

Topics in statistical mechanics

Autores: Boutillier, Cédric; Raschel, Kilian; de Tilière, Béatrice
Publicado en: Panoramas et Synthèses, Edición 59, 2023, ISBN 978-2-85629-970-8
Editor: Société Mathématique de France (SMF)

Transcendence in Algebra, Combinatorics, Geometry and Number Theory

Autores: Alin Bostan; Kilian Raschel
Publicado en: Springer Proceedings in Mathematics & Statistics, 2021, ISBN 978-3-030-84303-8
Editor: Cham: Springer
DOI: 10.1007/978-3-030-84304-5

Asymptotics of Minimal Deterministic FiniteAutomata Recognizing a Finite Binary Language

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

The combinatorial PT-DT correspondence

Autores: Jenne, Helen; Webb, Gautam; Young, Benjamin
Publicado en: Séminaire Lotharingien de Combinatoire, Edición 12864889, 2021, Página(s) Art. 89, 12, ISSN 1286-4889
Editor: Univ. Louis Pasteur Univ. Wien, Fak. Math.
DOI: 10.48550/arxiv.2012.08484

Polyharmonic Functions in the Quarter Plane

Autores: Nessmann, Andreas
Publicado en: Leibniz International Proceedings in Informatics (LIPIcs), Edición 225, 2022, Página(s) Article No. 15, 16 pp., ISBN 978-3-95977-230-3
Editor: Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern
DOI: 10.48550/arxiv.2212.07258

Polyharmonic functions and random processes in cones

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

Counting lattice walks by winding angle

Autores: Price, Andrew Elvey
Publicado en: Séminaire Lotharingien de Combinatoire, Edición 84B, Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics, 2020, Página(s) "Article #43, 12 pp.", ISSN 1286-4889
Editor: Univ. Louis Pasteur Univ. Wien, Fak. Math.

Eulerian orientations and the six-vertex model on planar maps

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

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