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

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Publications

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
DOI: 10.1007/s10231-020-00981-8

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
DOI: 10.5802/pmb.29

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

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

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
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
DOI: 10.1016/j.aam.2020.102043

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
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
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
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
DOI: 10.37236/8019

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
DOI: 10.1016/j.jcta.2020.105306

The six-vertex model on random planar maps revisited

Author(s): Andrew Elvey Price, Paul Zinn-Justin
Published in: Preprint, 2020

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

Author(s): Julien Courtiel, Andrew Elvey Price, Irène Marcovici
Published in: Preprint, 2020

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: Prepriny, 2020

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

Author(s): Peigné, Marc; Woess, Wolfgang
Published in: Preprint, 2019

Stieltjes moment sequences for pattern-avoiding permutations

Author(s): Elvey-Price, Andrew; Bostan, Alin; Guttmann, Anthony,; Maillard, Jean-Marie
Published in: arXiv, 2020

Martin boundary of random walks in convex cones

Author(s): Duraj, Jetlir; Raschel, Kilian; Tarrago, Pierre; Wachtel, Vitali
Published in: Preprint, 2020

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

Author(s): Franceschi, Sandro
Published in: Preprint, 2019

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

Author(s): Price, Andrew Elvey
Published in: Preprint, 2019

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

Author(s): Dreyfus, Thomas; Trotignon, Amélie
Published in: Preprint, 2020

Martin boundary of killed random walks on isoradial graphs

Author(s): Boutillier, Cédric; Raschel, Kilian; Bostan, Alin
Published in: Preprint, 2019

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
DOI: 10.4230/lipics.aofa.2020.11

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
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

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