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## 55

### Article dans une revue34 documents

• Olivier Bernardi, Mireille Bousquet-Mélou, Kilian Raschel. Counting quadrant walks via Tutte's invariant method. Combinatorial Theory, In press. ⟨hal-01577762v3⟩
• Cédric Boutillier, Kilian Raschel, Alin Bostan. Martin boundary of killed random walks on isoradial graphs. Potential Analysis, Springer Verlag, In press. ⟨hal-02422417v2⟩
• Mireille Bousquet-Mélou, Éric Fusy, Kilian Raschel. Plane bipolar orientations and quadrant walks. Seminaire Lotharingien de Combinatoire, Université Louis Pasteur, 2020, 81, pp.Article B81l. ⟨hal-02127624v2⟩
• Cédric Boutillier, Béatrice de Tilière, Kilian Raschel. The Z-invariant Ising model via dimers. Probability Theory and Related Fields, Springer Verlag, 2019, 174 (1-2), pp.235-305. ⟨10.1007/s00440-018-0861-x⟩. ⟨hal-01423324v2⟩
• Thomas Dreyfus, Kilian Raschel. Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks. Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, Publications mathématiques de Besançon, 2019, p. 41-80. ⟨hal-01591022v2⟩
• Kilian Raschel, Amélie Trotignon. On walks avoiding a quadrant. The Electronic Journal of Combinatorics, Open Journal Systems, 2019, 26 (3). ⟨hal-01848287v2⟩
• Gerold Alsmeyer, Kilian Raschel. The extinction problem for a class of distylous plant populations with sporophytic self-incompatibility. Journal of Mathematical Biology, Springer Verlag (Germany), 2019, 78 (6), pp.1841-1874. ⟨10.1007/s00285-019-01328-5⟩. ⟨hal-01895778v2⟩
• Alin Bostan, Alexander Marynych, Kilian Raschel. On the least common multiple of several random integers. Journal of Number Theory, Elsevier, 2019, 204, pp.113--133. ⟨10.1016/j.jnt.2019.03.017⟩. ⟨hal-01984389⟩
• Sandro Franceschi, Kilian Raschel. Integral expression for the stationary distribution of reflected Brownian motion in a wedge. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2019, 25 (4B), pp.3673-3713. ⟨10.3150/19-BEJ1107⟩. ⟨hal-01495788v3⟩
• Cédric Boutillier, Béatrice de Tilière, Kilian Raschel. The $Z$-invariant massive Laplacian on isoradial graphs. Inventiones Mathematicae, Springer Verlag, 2017, 208 (1), pp.109-189. ⟨10.1007/s00222-016-0687-z⟩. ⟨hal-01140329⟩
• Alin Bostan, Irina Kurkova, Kilian Raschel. A human proof of Gessel's lattice path conjecture. Transactions of the American Mathematical Society, American Mathematical Society, 2017, 369 (2, February 2017), pp.1365-1393. ⟨hal-00858083v3⟩
• J Courtiel, Stephen Melczer, Marni Mishna, Kilian Raschel. Weighted Lattice Walks and Universality Classes. Journal of Combinatorial Theory, Series A, Elsevier, 2017, ⟨10.1016/j.jcta.2017.06.008⟩. ⟨hal-01368786v2⟩
• Sandro Franceschi, Kilian Raschel. Tutte's invariant approach for Brownian motion reflected in the quadrant. ESAIM: Probability and Statistics, EDP Sciences, 2017, ESAIM: PS Volume 21, 2017, 21, pp.220-234. ⟨10.1051/ps/2017006⟩. ⟨hal-01271870v3⟩
• Rodolphe Garbit, Kilian Raschel. On the exit time from a cone for random walks with drift. Revista Matemática Iberoamericana, European Mathematical Society, 2016, 32 (2), pp.511-532. ⟨10.4171/rmi/893⟩. ⟨hal-00838721v5⟩
• Alin Bostan, Kilian Raschel. Compter les excursions sur un échiquier. Pour la science, Société Pour la Science 2015, pp.40-46. ⟨hal-01246339⟩
• Irina Kourkova, Kilian Raschel. New steps in walks with small steps in the quarter plane. Annals of Combinatorics, Springer Verlag, 2015, 19 (2015) (3), pp.461-511. ⟨10.1007/s00026-015-0279-4⟩. ⟨hal-00840239v2⟩
• Alin Bostan, Kilian Raschel, Bruno Salvy. Non-D-finite excursions in the quarter plane. Journal of Combinatorial Theory, Series A, Elsevier, 2014, 121, pp.45-63. ⟨10.1016/j.jcta.2013.09.005⟩. ⟨hal-00697386v2⟩
• Guy Fayolle, Kilian Raschel. About a possible analytic approach for walks in the quarter plane with arbitrary big jumps. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2014, C. R. Acad. Sci. Paris, Ser I, pp.6. ⟨10.1016/j.crma.2014.11.015⟩. ⟨hal-01021327⟩
• Rodolphe Garbit, Kilian Raschel. On the exit time from a cone for Brownian motion with drift. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2014, 19 (63), pp. 1-27. ⟨10.1214/EJP.v19-3169⟩. ⟨hal-00880523v2⟩
• Kilian Raschel. Random walks in the quarter plane, discrete harmonic functions and conformal mappings. Stochastic Processes and their Applications, Elsevier, 2014, 114 (10), pp.3147-3178. ⟨10.1016/j.spa.2014.04.013⟩. ⟨hal-00780452v2⟩
• Johan van Leeuwaarden, Kilian Raschel. Random walks reaching against all odds the other side of the quarter plane. Journal of Applied Probability, Cambridge University press, 2013, 50 (1), pp.85-102. ⟨10.1239/jap/1363784426⟩. ⟨hal-00586295v2⟩
• Irina Kourkova, Kilian Raschel. Passage time of a random walk in the quarter plane for opinions in the voter model. Queueing Systems, Springer Verlag, 2013, 74 (2-3), pp.219-234. ⟨10.1007/s11134-012-9333-7⟩. ⟨hal-00384187v4⟩
• Pauline Lafitte-Godillon, Kilian Raschel, Viet Chi Tran. Extinction probabilities for a distylous plant population modeled by an inhomogeneous random walk on the positive quadrant. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2013, 73 (2), pp.700-722. ⟨10.1137/120864258⟩. ⟨hal-00664536v2⟩
• Rim Essifi, Marc Peigné, Kilian Raschel. Some aspects of fluctuations of random walks on R and applications to random walks on R+ with non-elastic reflection at 0. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2013, 10 (2), pp.591-607. ⟨hal-00780453v2⟩
• Ivo Adan, Johan van Leeuwaarden, Kilian Raschel. The compensation approach for walks with small steps in the quarter plane. Combinatorics, Probability and Computing, Cambridge University Press (CUP), 2013, 22 (2), pp.161-183. ⟨10.1017/S0963548312000594⟩. ⟨hal-00551472v3⟩
• Kilian Raschel. Counting walks in a quadrant: a unified approach via boundary value problems. Journal of the European Mathematical Society, European Mathematical Society, 2012, 14, pp.749-777. ⟨hal-00461853v3⟩
• Irina Kurkova, Kilian Raschel. On the functions counting walks with small steps in the quarter plane. Publications Mathématiques de L'IHÉS, Springer Verlag, 2012, 116 (1), pp.69-114. ⟨10.1007/s10240-012-0045-7⟩. ⟨hal-00628424v2⟩
• Guy Fayolle, Kilian Raschel. Some exact asymptotics in the counting of walks in the quarter-plane. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, pp.109-124. ⟨hal-00765851⟩
• Kilian Raschel. Green functions for killed random walks in the Weyl chamber of Sp(4). Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2011, 47 (4), pp.1001-1019. ⟨hal-00425923v2⟩
• Irina Kurkova, Kilian Raschel. Random walks in Z_+^2 with non-zero drift absorbed at the axes. Bulletin de la société mathématique de France, Société Mathématique de France, 2011, 139 (3), pp.287-295. ⟨hal-00372260⟩
• Irina Kurkova, Kilian Raschel. Explicit expression for the generating function counting Gessel's walks. Advances in Applied Mathematics, Elsevier, 2011, 47, pp.414-433. ⟨hal-00438190v3⟩
• Guy Fayolle, Kilian Raschel. Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group. Markov Processes and Related Fields, Polymath, 2011, 17 (4), pp.619-636. ⟨inria-00572276⟩
• Kilian Raschel. Green functions and Martin compactification for killed random walks related to SU(3). Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2010, 15, pp.176-190. ⟨hal-00425651v2⟩
• Guy Fayolle, Kilian Raschel. On the Holonomy or Algebraicity of Generating Functions Counting Lattice Walks in the Quarter-Plane. Markov Processes and Related Fields, Polymath, 2010, 16 (3), pp.485-496. ⟨inria-00469603⟩

### Communication dans un congrès4 documents

• Francois Chapon, Eric Fusy, Kilian Raschel. Polyharmonic functions and random processes in cones. 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. ⟨hal-02436386v2⟩
• Olivier Bernardi, Mireille Bousquet-Mélou, Kilian Raschel. Counting quadrant walks via Tutte's invariant method (extended abstract). 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Jul 2016, Vancouver, Canada. ⟨hal-01228676v2⟩
• Sandro Franceschi, Irina Kurkova, Kilian Raschel. Analytic approach for reflected Brownian motion in the quadrant. International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Jul 2016, Cracovie, Poland. ⟨hal-01317611⟩
• Guy Fayolle, Kilian Raschel. Some exact asymptotics in the counting of walks in the quarter plane. 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. pp.109-124. ⟨hal-01197241⟩

### Ouvrage (y compris édition critique et traduction)1 document

• Alin Bostan, Kilian Raschel. Transcendence in Algebra, Combinatorics, Geometry and Number Theory. Springer, 373, 560 p., 2021, Springer Proceedings in Mathematics & Statistics, 978-3-030-84303-8. ⟨hal-03423170⟩

### Chapitre d'ouvrage1 document

• Cédric Lecouvey, Kilian Raschel. t-Martin boundary of killed random walks in the quadrant. 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⟩. ⟨hal-01199055v2⟩

### Direction d'ouvrage, Proceedings, Dossier2 documents

• Kilian Raschel, Ellen Saada. Large Random Networks and Constrained Random Walks, In honor of Guy Fayolle, on the occasion of his 75th birthday. Markov Processes and Related Fields, Volume 26, Number 4, 2020.. Kilian Raschel, Ellen Saada. Large Random Networks and Constrained Random Walks, In honor of Guy Fayolle, on the occasion of his 75th birthday, Aug 2018, Dijon, France. Markov Processes And Related Fields, 26 (4), Polymat Publishing Company, 535-778 (244 p.), 2020, Special Issue containing papers presented at the meeting: Large Random Networks and Constrained Random Walks, In honor of Guy Fayolle, on the occasion of his 75th birthday. ⟨hal-02996959⟩
• Mathias Beiglböck, Martin Huesmann, Florian Stebegg, Nicolas Juillet, Gilles Pagès, et al.. Séminaire de Probabilités XLVIII. Donati-Martin, Catherine; Lejay, Antoine; Rouault, Alain. France. 2168, Springer, pp.506, 2016, Lecture Notes in Mathematics, 978-3-319-44464-2. ⟨10.1007/978-3-319-44465-9⟩. ⟨hal-01403845⟩

### Pré-publication, Document de travail10 documents

• Rodolphe Garbit, Kilian Raschel. The generating function of the survival probabilities in a cone is not rational. 2021. ⟨hal-03418842v2⟩
• Guy Fayolle, Sandro Franceschi, Kilian Raschel. On the stationary distribution of reflected Brownian motion in a non-convex wedge. 2021. ⟨hal-03150317v2⟩
• Mireille Bousquet-Mélou, Andrew Elvey-Price, Sandro Franceschi, Charlotte Hardouin, Kilian Raschel. The stationary distribution of reflected Brownian motion in a wedge: differential properties. 2021. ⟨hal-03098489⟩
• Gerold Alsmeyer, Alin Bostan, Kilian Raschel, Thomas Simon. Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials. 2021. ⟨hal-03469594⟩
• Viet Hoang, Kilian Raschel, Pierre Tarrago. Constructing discrete harmonic functions in wedges. 2020. ⟨hal-02987609⟩
• Irina Ignatiouk-Robert, Irina Kourkova, Kilian Raschel. REFLECTED RANDOM WALKS AND UNSTABLE MARTIN BOUNDARY. 2020. ⟨hal-02982156⟩
• Alin Bostan, Lucia Di Vizio, Kilian Raschel. Differential transcendence of Bell numbers and relatives: a Galois theoretic approach. 2020. ⟨hal-03091272⟩
• Jetlir Duraj, Kilian Raschel, Pierre Tarrago, Vitali Wachtel. Martin boundary of random walks in convex cones. 2020. ⟨hal-02499786⟩
• Kilian Raschel, Pierre Tarrago. Boundary behavior of random walks in cones. 2020. ⟨hal-01895793v2⟩
• Kilian Raschel. Random walks in the quarter plane absorbed at the boundary: exact and asymptotic. 2009. ⟨hal-00361951⟩

### Rapport1 document

• Guy Fayolle, Kilian Raschel. Some exact asymptotics in the counting of walks in the quarter-plane. [Research Report] RR-7863, INRIA. 2012, pp.17. ⟨hal-00661541⟩

### Thèse1 document

• Kilian Raschel. Chemins confinés dans un quadrant. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2010. English. ⟨tel-00539964⟩

### HDR1 document

• Kilian Raschel. Combinatoire Elliptique et Marches dans des Cônes. Probabilités [math.PR]. Université de Tours / Région Centre, 2016. ⟨tel-01367986⟩