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# Kilian Raschel

54
Documents

## Publications

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

Markov Processes And Related Fields, 2022, Markov Processes ans Related Fields, 28 (5), pp.32
Journal articles

### Martin boundary of killed random walks on isoradial graphs

Potential Analysis, 2022, 57, pp.201-226. ⟨10.1007/s11118-021-09912-5⟩
Journal articles

Journal articles

### Counting quadrant walks via Tutte's invariant method

Combinatorial Theory, 2021, 1, paper # 3
Journal articles

### Plane bipolar orientations and quadrant walks

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

### On walks avoiding a quadrant

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

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

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

### On the least common multiple of several random integers

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

### The extinction problem for a class of distylous plant populations with sporophytic self-incompatibility

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

### Integral expression for the stationary distribution of reflected Brownian motion in a wedge

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

### The Z-invariant Ising model via dimers

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

### Weighted Lattice Walks and Universality Classes

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

### The $Z$-invariant massive Laplacian on isoradial graphs

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

### Tutte's invariant approach for Brownian motion reflected in the quadrant

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

### A human proof of Gessel's lattice path conjecture

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

### On the exit time from a cone for random walks with drift

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

### New steps in walks with small steps in the quarter plane

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

### Compter les excursions sur un échiquier

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

### On the exit time from a cone for Brownian motion with drift

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

### Non-D-finite excursions in the quarter plane

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

### 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, 2014, C. R. Acad. Sci. Paris, Ser I, CRASS1:5432, pp.6. ⟨10.1016/j.crma.2014.11.015⟩
Journal articles

### Random walks in the quarter plane, discrete harmonic functions and conformal mappings

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

### The compensation approach for walks with small steps in the quarter plane

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

### Passage time of a random walk in the quarter plane for opinions in the voter model

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

### Extinction probabilities for a distylous plant population modeled by an inhomogeneous random walk on the positive quadrant

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

### Random walks reaching against all odds the other side of the quarter plane

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

### 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, 2013, 10 (2), pp.591-607
Journal articles

### Some exact asymptotics in the counting of walks in the quarter-plane

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

### Counting walks in a quadrant: a unified approach via boundary value problems

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

### On the functions counting walks with small steps in the quarter plane

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

### Random walks in Z_+^2 with non-zero drift absorbed at the axes

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

### Explicit expression for the generating function counting Gessel's walks

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

### Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group

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

### Green functions for killed random walks in the Weyl chamber of Sp(4)

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

### Green functions and Martin compactification for killed random walks related to SU(3)

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

### On the Holonomy or Algebraicity of Generating Functions Counting Lattice Walks in the Quarter-Plane

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

### 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
Conference papers

### 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. ⟨10.46298/dmtcs.6416⟩
Conference papers

### 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
Conference papers

### 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, ⟨10.46298/dmtcs.2988⟩
Conference papers

### Transcendence in Algebra, Combinatorics, Geometry and Number Theory

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

### Séminaire de Probabilités XLVIII

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⟩
Books

### 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⟩
Book sections

### Chemins confinés dans un quadrant

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

### Combinatoire Elliptique et Marches dans des Cônes

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