Kilian Raschel

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Publications

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

Mireille Bousquet-Mélou , Andrew Elvey Price , Sandro Franceschi , Charlotte Hardouin , Kilian Raschel

Electronic Journal of Probability, 2025, 30, pp.1-68. ⟨10.1214/24-EJP1257⟩

Article dans une revue hal-03098489v2
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On the first hitting time of a high-dimensional orthant

Emmanuel Humbert , Kilian Raschel

Electronic Communications in Probability, 2025, 30, pp.39. ⟨10.1214/25-ECP688⟩

Article dans une revue hal-05220909v1
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Some topics in random walks

Quentin Berger , Celine Bonnet , Lucile Laulin , Kilian Raschel

ESAIM: Proceedings and Surveys, 2025, Journées MAS 2022 - Dynamic and Stochastic Modelling Rouen, France, August 29–31, 2022, 80, pp.51-71. ⟨10.1051/proc/202580051⟩

Article dans une revue hal-05210861v1
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Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent

Luc Hillairet , Helen Jenne , Kilian Raschel

Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2024, 11 (4), pp.683-713. ⟨10.4171/AIHPD/184⟩

Article dans une revue hal-03470460v1
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On the limit law of the superdiffusive elephant random walk

Hélène Guérin , Lucile Laulin , Kilian Raschel , Thomas Simon

Electronic Journal of Probability, 2024, 30 (none), ⟨10.48550/arXiv.2409.06836⟩

Article dans une revue hal-04700888v1
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Logarithmic terms in discrete heat kernel expansions in the quadrant

Andrew Elvey Price , Andreas Nessmann , Kilian Raschel

Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2024, ⟨10.4171/AIHPD/199⟩

Article dans une revue hal-04270378v1
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Differential transcendence of Bell numbers and relatives: a Galois theoretic approach

Alin Bostan , Lucia Di Vizio , Kilian Raschel

American Journal of Mathematics, 2024, 146 (6), pp.1577-1615. ⟨10.1353/ajm.2024.a944358⟩

Article dans une revue hal-03091272v3
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Multivariate Multiplicative Functions of Uniform Random Vectors in Large Integer Domains

Zakhar Kabluchko , Alexander Marynych , Kilian Raschel

Results in mathematics = Resultate der Mathematik, 2023, 78 (5), pp.201. ⟨10.1007/s00025-023-01978-4⟩

Article dans une revue hal-04671556v1
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Harmonic functions for singular quadrant walks

Viet Hung Hoang , Kilian Raschel , Pierre Tarrago

Indagationes Mathematicae, 2023, 34, pp.936-972. ⟨10.1016/j.indag.2023.06.002⟩

Article dans une revue hal-03913217v1
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The generating function of the survival probabilities in a cone is not rational

Rodolphe Garbit , Kilian Raschel

Séminaire Lotharigien de Combinatoire, 2023, 87B, ⟨10.48550/arXiv.2111.05027⟩

Article dans une revue hal-03418842v2
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Random walks with drift inside a pyramid: convergence rate for the survival probability

Rodolphe Garbit , Kilian Raschel

ALEA : Latin American Journal of Probability and Mathematical Statistics, 2023, 20 (2), pp.973. ⟨10.30757/ALEA.v20-35⟩

Article dans une revue hal-03879363v2
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Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials

Gerold Alsmeyer , Alin Bostan , Kilian Raschel , Thomas Simon

Advances in Applied Mathematics, 2023, ⟨10.1016/j.aam.2023.102555⟩

Article dans une revue hal-03469594v1
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Stationary brownian motion in a 3/4-plane: Reduction to a riemann-hilbert problem via fourier transforms

Guy Fayolle , Sandro Franceschi , Kilian Raschel

Indagationes Mathematicae, 2023, 34 (5), pp.17 (874-890). ⟨10.1016/j.indag.2022.10.008⟩

Article dans une revue hal-03832431v2
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Constructing discrete harmonic functions in wedges

Viet Hung Hoang , Kilian Raschel , Pierre Tarrago

Transactions of the American Mathematical Society, 2022, 375 (7), pp.4741-4782. ⟨10.1090/tran/8615⟩

Article dans une revue hal-02987609v2
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On the stationary distribution of reflected Brownian motion in a non-convex wedge

Guy Fayolle , Sandro Franceschi , Kilian Raschel

Markov Processes And Related Fields, 2022, Markov Processes ans Related Fields, 28 (5), pp.737-772. ⟨10.48550/arXiv.2102.11754⟩

Article dans une revue hal-03150317v3
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Martin boundary of killed random walks on isoradial graphs

Cédric Boutillier , Kilian Raschel , Alin Bostan

Potential Analysis, 2022, 57 (2), pp.201-226. ⟨10.1007/s11118-021-09912-5⟩

Article dans une revue hal-02422417v2
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Martin boundary of random walks in convex cones

Jetlir Duraj , Kilian Raschel , Pierre Tarrago , Vitali Wachtel

Annales Henri Lebesgue, 2022, 5, pp.559-609. ⟨10.5802/ahl.130⟩

Article dans une revue hal-02499786v1
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Counting quadrant walks via Tutte's invariant method

Olivier Bernardi , Mireille Bousquet-Mélou , Kilian Raschel

Combinatorial Theory, 2021, 1, paper # 3. ⟨10.5070/C61055360⟩

Article dans une revue hal-01577762v3
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Plane bipolar orientations and quadrant walks

Mireille Bousquet-Mélou , Éric Fusy , Kilian Raschel

Seminaire Lotharingien de Combinatoire, 2020, 81, pp.Article B81l

Article dans une revue hal-02127624v2
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Boundary behavior of random walks in cones

Kilian Raschel , Pierre Tarrago

Markov Processes And Related Fields, 2020, 26 (4), pp.711-756

Article dans une revue hal-01895793v2
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On the least common multiple of several random integers

Alin Bostan , Alexander Marynych , Kilian Raschel

Journal of Number Theory, 2019, 204, pp.113--133. ⟨10.1016/j.jnt.2019.03.017⟩

Article dans une revue hal-01984389v1
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On walks avoiding a quadrant

Kilian Raschel , Amélie Trotignon

The Electronic Journal of Combinatorics, 2019, 26 (3)

Article dans une revue hal-01848287v2
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The Z-invariant Ising model via dimers

Cédric Boutillier , Béatrice de Tilière , Kilian Raschel

Probability Theory and Related Fields, 2019, 174 (1-2), pp.235-305. ⟨10.1007/s00440-018-0861-x⟩

Article dans une revue hal-01423324v2
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Integral expression for the stationary distribution of reflected Brownian motion in a wedge

Sandro Franceschi , Kilian Raschel

Bernoulli, 2019, 25 (4B), pp.3673-3713. ⟨10.3150/19-BEJ1107⟩

Article dans une revue hal-01495788v3
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Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks

Thomas Dreyfus , Kilian Raschel

Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres, 2019, p. 41-80. ⟨10.5802/pmb.29⟩

Article dans une revue hal-01591022v2
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The extinction problem for a class of distylous plant populations with sporophytic self-incompatibility

Gerold Alsmeyer , Kilian Raschel

Journal of Mathematical Biology, 2019, 78 (6), pp.1841-1874. ⟨10.1007/s00285-019-01328-5⟩

Article dans une revue hal-01895778v2

The $Z$-invariant massive Laplacian on isoradial graphs

Cédric Boutillier , Béatrice de Tilière , Kilian Raschel

Inventiones Mathematicae, 2017, 208 (1), pp.109-189. ⟨10.1007/s00222-016-0687-z⟩

Article dans une revue hal-01140329v1
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Weighted Lattice Walks and Universality Classes

J Courtiel , Stephen Melczer , Marni Mishna , Kilian Raschel

Journal of Combinatorial Theory, Series A, 2017, ⟨10.1016/j.jcta.2017.06.008⟩

Article dans une revue hal-01368786v2
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Tutte's invariant approach for Brownian motion reflected in the quadrant

Sandro Franceschi , Kilian Raschel

ESAIM: Probability and Statistics, 2017, ESAIM: PS Volume 21, 2017, 21, pp.220-234. ⟨10.1051/ps/2017006⟩

Article dans une revue hal-01271870v3
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A human proof of Gessel's lattice path conjecture

Alin Bostan , Irina Kurkova , Kilian Raschel

Transactions of the American Mathematical Society, 2017, 369 (2, February 2017), pp.1365-1393

Article dans une revue hal-00858083v3
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On the exit time from a cone for random walks with drift

Rodolphe Garbit , Kilian Raschel

Revista Matemática Iberoamericana, 2016, 32 (2), pp.511-532. ⟨10.4171/rmi/893⟩

Article dans une revue hal-00838721v5

Compter les excursions sur un échiquier

Alin Bostan , Kilian Raschel

Pour la science, 2015, 449, pp.40-46

Article dans une revue hal-01246339v1
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New steps in walks with small steps in the quarter plane

Irina Kourkova , Kilian Raschel

Annals of Combinatorics, 2015, 19 (2015) (3), pp.461-511. ⟨10.1007/s00026-015-0279-4⟩

Article dans une revue hal-00840239v2
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About a possible analytic approach for walks in the quarter plane with arbitrary big jumps

Guy Fayolle , Kilian Raschel

Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2014, C. R. Acad. Sci. Paris, Ser I, CRASS1:5432, pp.6. ⟨10.1016/j.crma.2014.11.015⟩

Article dans une revue hal-01021327v1
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Random walks in the quarter plane, discrete harmonic functions and conformal mappings

Kilian Raschel

Stochastic Processes and their Applications, 2014, 114 (10), pp.3147-3178. ⟨10.1016/j.spa.2014.04.013⟩

Article dans une revue hal-00780452v2
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Non-D-finite excursions in the quarter plane

Alin Bostan , Kilian Raschel , Bruno Salvy

Journal of Combinatorial Theory, Series A, 2014, 121, pp.45-63. ⟨10.1016/j.jcta.2013.09.005⟩

Article dans une revue hal-00697386v2
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On the exit time from a cone for Brownian motion with drift

Rodolphe Garbit , Kilian Raschel

Electronic Journal of Probability, 2014, 19 (63), pp. 1-27. ⟨10.1214/EJP.v19-3169⟩

Article dans une revue hal-00880523v2
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Some aspects of fluctuations of random walks on R and applications to random walks on R+ with non-elastic reflection at 0

Rim Essifi , Marc Peigné , Kilian Raschel

ALEA : Latin American Journal of Probability and Mathematical Statistics, 2013, 10 (2), pp.591-607

Article dans une revue hal-00780453v2
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Random walks reaching against all odds the other side of the quarter plane

Johan van Leeuwaarden , Kilian Raschel

Journal of Applied Probability, 2013, 50 (1), pp.85-102. ⟨10.1239/jap/1363784426⟩

Article dans une revue hal-00586295v2
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Passage time of a random walk in the quarter plane for opinions in the voter model

Irina Kourkova , Kilian Raschel

Queueing Systems, 2013, 74 (2-3), pp.219-234. ⟨10.1007/s11134-012-9333-7⟩

Article dans une revue hal-00384187v4
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Extinction probabilities for a distylous plant population modeled by an inhomogeneous random walk on the positive quadrant

Pauline Lafitte-Godillon , Kilian Raschel , Viet Chi Tran

SIAM Journal on Applied Mathematics, 2013, 73 (2), pp.700-722. ⟨10.1137/120864258⟩

Article dans une revue hal-00664536v2
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The compensation approach for walks with small steps in the quarter plane

Ivo Adan , Johan van Leeuwaarden , Kilian Raschel

Combinatorics, Probability and Computing, 2013, 22 (2), pp.161-183. ⟨10.1017/S0963548312000594⟩

Article dans une revue hal-00551472v3
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Counting walks in a quadrant: a unified approach via boundary value problems

Kilian Raschel

Journal of the European Mathematical Society, 2012, 14, pp.749-777

Article dans une revue hal-00461853v3
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Some exact asymptotics in the counting of walks in the quarter-plane

Guy Fayolle , Kilian Raschel

Discrete Mathematics and Theoretical Computer Science, 2012, pp.109-124

Article dans une revue hal-00765851v1
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On the functions counting walks with small steps in the quarter plane

Irina Kurkova , Kilian Raschel

Publications Mathématiques de L'IHÉS, 2012, 116 (1), pp.69-114. ⟨10.1007/s10240-012-0045-7⟩

Article dans une revue hal-00628424v2
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Explicit expression for the generating function counting Gessel's walks

Irina Kurkova , Kilian Raschel

Advances in Applied Mathematics, 2011, 47, pp.414-433

Article dans une revue hal-00438190v3
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Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group

Guy Fayolle , Kilian Raschel

Markov Processes And Related Fields, 2011, 17 (4), pp.619-636

Article dans une revue inria-00572276v1
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Green functions for killed random walks in the Weyl chamber of Sp(4)

Kilian Raschel

Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2011, 47 (4), pp.1001-1019

Article dans une revue hal-00425923v2
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Random walks in Z_+^2 with non-zero drift absorbed at the axes

Irina Kurkova , Kilian Raschel

Bulletin de la société mathématique de France, 2011, 139 (3), pp.287-295

Article dans une revue hal-00372260v1
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On the Holonomy or Algebraicity of Generating Functions Counting Lattice Walks in the Quarter-Plane

Guy Fayolle , Kilian Raschel

Markov Processes And Related Fields, 2010, 16 (3), pp.485-496

Article dans une revue inria-00469603v1
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Green functions and Martin compactification for killed random walks related to SU(3)

Kilian Raschel

Electronic Communications in Probability, 2010, 15 (17), pp.176-190

Article dans une revue hal-00425651v2
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Polyharmonic functions and random processes in cones

Francois Chapon , Eric Fusy , Kilian Raschel

31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020), Clemens Heuberger, Jun 2020, Klagenfurt, Austria. pp.9:1--9:19

Communication dans un congrès hal-02436386v2
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Counting quadrant walks via Tutte's invariant method (extended abstract)

Olivier Bernardi , Mireille Bousquet-Mélou , Kilian Raschel

28-th International Conference on Formal Power Series and Algebraic Combinatorics, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6416⟩

Communication dans un congrès hal-01228676v2
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Analytic approach for reflected Brownian motion in the quadrant

Sandro Franceschi , Irina Kurkova , Kilian Raschel

International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Jul 2016, Cracovie, Poland

Communication dans un congrès hal-01317611v1
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Some exact asymptotics in the counting of walks in the quarter plane

Guy Fayolle , Kilian Raschel

23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. pp.109-124, ⟨10.46298/dmtcs.2988⟩

Communication dans un congrès hal-01197241v1

Topics in statistical mechanics

Cédric Boutillier , Béatrice de Tilière , Kilian Raschel

Société Mathématique de France. Société Mathématique de France, 59, pp.xxii + 230, 2023, Panoramas et Synthèses, Anne Moreau, 978-2-85629-970-8

Ouvrages (ouvrage de synthèse) hal-04270409v1

Transcendence in Algebra, Combinatorics, Geometry and Number Theory

Alin Bostan , Kilian Raschel

Springer, 373, 560 p., 2021, Springer Proceedings in Mathematics & Statistics, 978-3-030-84303-8

Ouvrages hal-03423170v1

Séminaire de Probabilités XLVIII

Mathias Beiglböck , Martin Huesmann , Florian Stebegg , Nicolas Juillet , Gilles Pagès et al.

Donati-Martin, Catherine; Lejay, Antoine; Rouault, Alain. Springer, 2168, pp.506, 2016, Lecture Notes in Mathematics, 978-3-319-44464-2. ⟨10.1007/978-3-319-44465-9⟩

Ouvrages hal-01403845v1
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t-Martin boundary of killed random walks in the quadrant

Cédric Lecouvey , Kilian Raschel

Catherine Donati-Martin; Antoine Lejay; Alain Rouault. Séminaire de Probabilités XLVIII, Volume 2168 of the series Lecture Notes in Mathematics Springer, pp.305-323, 2016, Séminaire de Probabilités XLVIII, 978-3-319-44464-2. ⟨10.1007/978-3-319-44465-9_11⟩

Chapitre d'ouvrage hal-01199055v2
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Singular walks in the quarter plane and Bernoulli numbers

Alin Bostan , Lucia Di Vizio , Kilian Raschel

2025

Pré-publication, Document de travail hal-05172463v1
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DISCRETE HARMONIC POLYNOMIALS IN MULTIDIMENSIONAL ORTHANTS

Emmanuel Humbert , Kilian Raschel

2025

Pré-publication, Document de travail hal-05061259v1
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Asymptotics of returns to the coordinate hyperplanes for conditioned simple random walks

Rodolphe Garbit , Kilian Raschel

2026

Pré-publication, Document de travail hal-05542357v1
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Persistence probabilities for MA(1) sequences with uniform innovations

Frank Aurzada , Kilian Raschel

2025

Pré-publication, Document de travail hal-05220903v1
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Boundary contacts for reflected random walks in the quarter plane

Viet Hung Hoang , Kilian Raschel

2025

Pré-publication, Document de travail hal-05220899v1
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Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness

Thomas Dreyfus , Andrew Elvey Price , Kilian Raschel

2024

Pré-publication, Document de travail hal-04801813v1
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Reflected random walks and unstable Martin boundary

Irina Ignatiouk-Robert , Irina Kourkova , Kilian Raschel

2022

Pré-publication, Document de travail hal-02982156v2

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

Alexander Iksanov , Alexander Marynych , Kilian Raschel

2021

Pré-publication, Document de travail hal-03501402v1
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Random walks in the quarter plane absorbed at the boundary: exact and asymptotic

Kilian Raschel

2009

Pré-publication, Document de travail hal-00361951v1
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Some exact asymptotics in the counting of walks in the quarter-plane

Guy Fayolle , Kilian Raschel

[Research Report] RR-7863, INRIA. 2012, pp.17

Rapport (rapport de recherche) hal-00661541v1
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Chemins confinés dans un quadrant

Kilian Raschel

Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2010. English. ⟨NNT : ⟩

Thèse tel-00539964v1
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Combinatoire Elliptique et Marches dans des Cônes

Kilian Raschel

Probabilités [math.PR]. Université de Tours / Région Centre, 2016

HDR tel-01367986v1