Franceschi, Sandro; Ichiba, Tomoyuki; Karatzas, Ioannis; Raschel, Kilian Invariant measure of gaps in degenerate competing three-particle systems. arXiv:2401.10734 Preprint, arXiv:2401.10734 [math.PR] (2024). BibTeX Cite \textit{S. Franceschi} et al., ``Invariant measure of gaps in degenerate competing three-particle systems'', Preprint, arXiv:2401.10734 [math.PR] (2024) Full Text: arXiv OA License
Guérin, Hélène; Laulin, Lucile; Raschel, Kilian Elephant polynomials. arXiv:2401.04959 Preprint, arXiv:2401.04959 [math.CO] (2024). BibTeX Cite \textit{H. Guérin} et al., ``Elephant polynomials'', Preprint, arXiv:2401.04959 [math.CO] (2024) Full Text: arXiv OA License
Garbit, Rodolphe; Raschel, Kilian Random walks with drift inside a pyramid: convergence rate for the survival probability. (English) Zbl 07799677 ALEA, Lat. Am. J. Probab. Math. Stat. 20, No. 2, 973-988 (2023). MSC: 60G50 60G40 60E10 52B11 PDFBibTeX XMLCite \textit{R. Garbit} and \textit{K. Raschel}, ALEA, Lat. Am. J. Probab. Math. Stat. 20, No. 2, 973--988 (2023; Zbl 07799677) Full Text: arXiv Link
Kabluchko, Zakhar; Marynych, Alexander; Raschel, Kilian Multivariate multiplicative functions of uniform random vectors in large integer domains. (English) Zbl 07732345 Result. Math. 78, No. 5, Paper No. 201, 22 p. (2023). MSC: 11K65 60F05 11N60 PDFBibTeX XMLCite \textit{Z. Kabluchko} et al., Result. Math. 78, No. 5, Paper No. 201, 22 p. (2023; Zbl 07732345) Full Text: DOI arXiv
Viet Hung Hoang; Raschel, Kilian; Tarrago, Pierre Harmonic functions for singular quadrant walks. (English) Zbl 1524.60090 Indag. Math., New Ser. 34, No. 5, 936-972 (2023). MSC: 60G50 60K25 05A15 60J65 PDFBibTeX XMLCite \textit{Viet Hung Hoang} et al., Indag. Math., New Ser. 34, No. 5, 936--972 (2023; Zbl 1524.60090) Full Text: DOI arXiv
Fayolle, Guy; Franceschi, Sandro; Raschel, Kilian Stationary Brownian motion in a \(3 / 4\)-plane: reduction to a Riemann-Hilbert problem via Fourier transforms. (English) Zbl 1522.35353 Indag. Math., New Ser. 34, No. 5, 874-890 (2023). MSC: 35Q15 60J65 44A10 42A38 35R10 35R60 PDFBibTeX XMLCite \textit{G. Fayolle} et al., Indag. Math., New Ser. 34, No. 5, 874--890 (2023; Zbl 1522.35353) Full Text: DOI arXiv
Boutillier, Cédric (ed.); de Tilière, Béatrice (ed.); Raschel, Kilian (ed.) Topics in statistical mechanics. (French) Zbl 1516.82003 Panoramas et Synthèses 59. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-970-8/pbk). xxii, 229 p. (2023). MSC: 82-06 15-06 60-06 15B52 28A80 60K35 81T40 82B20 82B27 82B40 82B44 82C05 82D60 PDFBibTeX XMLCite \textit{C. Boutillier} (ed.) et al., Topics in statistical mechanics. Paris: Société Mathématique de France (SMF) (2023; Zbl 1516.82003)
Alsmeyer, Gerold; Bostan, Alin; Raschel, Kilian; Simon, Thomas Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials. (English) Zbl 07711461 Adv. Appl. Math. 150, Article ID 102555, 52 p. (2023). MSC: 62-XX 05-XX 11B37 30C15 PDFBibTeX XMLCite \textit{G. Alsmeyer} et al., Adv. Appl. Math. 150, Article ID 102555, 52 p. (2023; Zbl 07711461) Full Text: DOI arXiv
Raschel, Kilian; Tarrago, Pierre Random walls in a cone and discrete harmonic functions. (Marches aléatoires dans un cône et fonctions discrètes harmoniques.) (French) Zbl 1525.60054 Gaz. Math., Soc. Math. Fr. 175, 35-48 (2023). MSC: 60G50 PDFBibTeX XMLCite \textit{K. Raschel} and \textit{P. Tarrago}, Gaz. Math., Soc. Math. Fr. 175, 35--48 (2023; Zbl 1525.60054)
Elvey-Price, Andrew; Nessmann, Andreas; Raschel, Kilian Logarithmic terms in discrete heat kernel expansions in the quadrant. arXiv:2309.15209 Preprint, arXiv:2309.15209 [math.CO] (2023). MSC: 05A16 05A15 05C81 31A30 35K08 BibTeX Cite \textit{A. Elvey-Price} et al., ``Logarithmic terms in discrete heat kernel expansions in the quadrant'', Preprint, arXiv:2309.15209 [math.CO] (2023) Full Text: arXiv OA License
Guérin, Hélène; Laulin, Lucile; Raschel, Kilian A fixed-point equation approach for the superdiffusive elephant random walk. arXiv:2308.14630 Preprint, arXiv:2308.14630 [math.PR] (2023). MSC: 60E05 60E10 60J10 60G50 BibTeX Cite \textit{H. Guérin} et al., ``A fixed-point equation approach for the superdiffusive elephant random walk'', Preprint, arXiv:2308.14630 [math.PR] (2023) Full Text: arXiv OA License
Kabluchko, Zakhar; Marynych, Alexander; Raschel, Kilian Random Walks in the High-Dimensional Limit II: The Crinkled Subordinator. arXiv:2306.04747 Preprint, arXiv:2306.04747 [math.PR] (2023). MSC: 60F05 60G50 60D05 60G51 BibTeX Cite \textit{Z. Kabluchko} et al., ``Random Walks in the High-Dimensional Limit II: The Crinkled Subordinator'', Preprint, arXiv:2306.04747 [math.PR] (2023) Full Text: arXiv OA License
Franceschi, Sandro; Raschel, Kilian A dual skew symmetry for transient reflected Brownian motion in an orthant. (English) Zbl 1501.60047 Queueing Syst. 102, No. 1-2, 123-141 (2022). MSC: 60J65 PDFBibTeX XMLCite \textit{S. Franceschi} and \textit{K. Raschel}, Queueing Syst. 102, No. 1--2, 123--141 (2022; Zbl 1501.60047) Full Text: DOI arXiv
Iksanov, Alexander; Marynych, Alexander; Raschel, Kilian Asymptotics of arithmetic functions of GCD and LCM of random integers in hyperbolic regions. (English) Zbl 1503.11128 Result. Math. 77, No. 4, Paper No. 165, 22 p. (2022). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N37 11A05 60F05 11A25 PDFBibTeX XMLCite \textit{A. Iksanov} et al., Result. Math. 77, No. 4, Paper No. 165, 22 p. (2022; Zbl 1503.11128) Full Text: DOI arXiv
Boutillier, Cédric; Raschel, Kilian Martin boundary of killed random walks on isoradial graphs. (English) Zbl 1496.31006 Potential Anal. 57, No. 2, 201-226 (2022). Reviewer: Marius Ghergu (Dublin) MSC: 31C35 05C81 82B20 60J45 PDFBibTeX XMLCite \textit{C. Boutillier} and \textit{K. Raschel}, Potential Anal. 57, No. 2, 201--226 (2022; Zbl 1496.31006) Full Text: DOI arXiv HAL
Hoang, Viet Hung; Raschel, Kilian; Tarrago, Pierre Constructing discrete harmonic functions in wedges. (English) Zbl 1496.31004 Trans. Am. Math. Soc. 375, No. 7, 4741-4782 (2022). Reviewer: Marius Ghergu (Dublin) MSC: 31C05 39A12 PDFBibTeX XMLCite \textit{V. H. Hoang} et al., Trans. Am. Math. Soc. 375, No. 7, 4741--4782 (2022; Zbl 1496.31004) Full Text: DOI arXiv
Duraj, Jetlir; Raschel, Kilian; Tarrago, Pierre; Wachtel, Vitali Martin boundary of random walks in convex cones. (Frontière de Martin de marches aléatoires dans des cônes convexes.) (English. French summary) Zbl 1492.60123 Ann. Henri Lebesgue 5, 559-609 (2022). MSC: 60G50 60G40 60F17 PDFBibTeX XMLCite \textit{J. Duraj} et al., Ann. Henri Lebesgue 5, 559--609 (2022; Zbl 1492.60123) Full Text: DOI arXiv
Raschel, Kilian; Tarrago, Pierre Marches aléatoires dans un cône et fonctions discrètes harmoniques. arXiv:2211.02925 Preprint, arXiv:2211.02925 [math.PR] (2022). BibTeX Cite \textit{K. Raschel} and \textit{P. Tarrago}, ``Marches al\'eatoires dans un c\^one et fonctions discr\`etes harmoniques'', Preprint, arXiv:2211.02925 [math.PR] (2022) Full Text: arXiv OA License
Bernardi, Olivier; Bousquet-Mélou, Mireille; Raschel, Kilian Counting quadrant walks via Tutte’s invariant method. (English) Zbl 1498.05012 Combinatorial Theory 1, Paper No. 3, 77 p. (2021). MSC: 05A15 39A06 30C20 30D05 PDFBibTeX XMLCite \textit{O. Bernardi} et al., Comb. Theory 1, Paper No. 3, 77 p. (2021; Zbl 1498.05012) Full Text: DOI arXiv
Bostan, Alin (ed.); Raschel, Kilian (ed.) Transcendence in algebra, combinatorics, geometry and number theory. TRANS19 – transient transcendence in Transylvania, Brașov, Romania, May 13–17, 2019. Revised and extended contributions. (English) Zbl 1478.11004 Springer Proceedings in Mathematics & Statistics 373. Cham: Springer (ISBN 978-3-030-84303-8/hbk; 978-3-030-84304-5/ebook). xxxix, 521 p. (2021). MSC: 11-06 11Jxx 00B25 PDFBibTeX XMLCite \textit{A. Bostan} (ed.) and \textit{K. Raschel} (ed.), Transcendence in algebra, combinatorics, geometry and number theory. TRANS19 -- transient transcendence in Transylvania, Brașov, Romania, May 13--17, 2019. Revised and extended contributions. Cham: Springer (2021; Zbl 1478.11004) Full Text: DOI
Fayolle, Guy; Franceschi, Sandro; Raschel, Kilian On the stationary distribution of reflected Brownian motion in a non-convex wedge. arXiv:2102.11754 Preprint, arXiv:2102.11754 [math.PR] (2021). MSC: 60J65 60E10 60H05 BibTeX Cite \textit{G. Fayolle} et al., ``On the stationary distribution of reflected Brownian motion in a non-convex wedge'', Preprint, arXiv:2102.11754 [math.PR] (2021) Full Text: arXiv OA License
Bousquet-Mélou, M.; Price, A. Elvey; Franceschi, S.; Hardouin, C.; Raschel, K. On the stationary distribution of reflected Brownian motion in a wedge: differential properties. arXiv:2101.01562 Preprint, arXiv:2101.01562 [math.PR] (2021). MSC: 60-XX 05-XX BibTeX Cite \textit{M. Bousquet-Mélou} et al., ``On the stationary distribution of reflected Brownian motion in a wedge: differential properties'', Preprint, arXiv:2101.01562 [math.PR] (2021) Full Text: arXiv OA License
Hillairet, Luc; Jenne, Helen; Raschel, Kilian Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent. arXiv:2112.03567 Preprint, arXiv:2112.03567 [math.CO] (2021). BibTeX Cite \textit{L. Hillairet} et al., ``Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent'', Preprint, arXiv:2112.03567 [math.CO] (2021) Full Text: arXiv OA License
Garbit, Rodolphe; Raschel, Kilian The generating function of the survival probabilities in a cone is not rational. arXiv:2111.05027 Preprint, arXiv:2111.05027 [math.CO] (2021). BibTeX Cite \textit{R. Garbit} and \textit{K. Raschel}, ``The generating function of the survival probabilities in a cone is not rational'', Preprint, arXiv:2111.05027 [math.CO] (2021) Full Text: arXiv OA License
Chapon, François; Fusy, Éric; Raschel, Kilian Polyharmonic functions and random processes in cones. (English) Zbl 07651048 Drmota, Michael (ed.) et al., 31st international conference on probabilistic, combinatorial and asymptotic methods for the analysis of algorithms, AofA 2020, Klagenfurt, Austria (virtual conference), June 15–19, 2020. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 159, Article 9, 19 p. (2020). MSC: 68W40 PDFBibTeX XMLCite \textit{F. Chapon} et al., LIPIcs -- Leibniz Int. Proc. Inform. 159, Article 9, 19 p. (2020; Zbl 07651048) Full Text: DOI arXiv
Raschel, Kilian; Tarrago, Pierre Boundary behavior of random walks in cones. (English) Zbl 1456.60110 Markov Process. Relat. Fields 26, No. 4, 711-756 (2020). MSC: 60G50 60G40 60F17 PDFBibTeX XMLCite \textit{K. Raschel} and \textit{P. Tarrago}, Markov Process. Relat. Fields 26, No. 4, 711--756 (2020; Zbl 1456.60110) Full Text: arXiv Link
Bernardi, Olivier; Bousquet-Mélou, Mireille; Raschel, Kilian Counting quadrant walks via Tutte’s invariant method (extended abstract). (English. French summary) Zbl 1440.05019 Proceedings of the 28th international conference on formal power series and algebraic combinatorics, FPSAC 2016, Vancouver, Canada, July 4–8, 2016. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Math. Theor. Comput. Sci., Proc., Article 6416, 14 p. (2020). MSC: 05A15 05C15 05C30 PDFBibTeX XMLCite \textit{O. Bernardi} et al., in: Proceedings of the 28th international conference on formal power series and algebraic combinatorics, FPSAC 2016, Vancouver, Canada, July 4--8, 2016. Nancy: The Association. Discrete Mathematics \& Theoretical Computer Science (DMTCS). Article 6416, 14 p. (2020; Zbl 1440.05019) Full Text: arXiv Link
Bogosel, B.; Perrollaz, V.; Raschel, K.; Trotignon, A. 3D positive lattice walks and spherical triangles. (English) Zbl 1433.05025 J. Comb. Theory, Ser. A 172, Article ID 105189, 47 p. (2020). MSC: 05A16 60G50 60F05 PDFBibTeX XMLCite \textit{B. Bogosel} et al., J. Comb. Theory, Ser. A 172, Article ID 105189, 47 p. (2020; Zbl 1433.05025) Full Text: DOI arXiv
Ignatiouk-Robert, Irina; Kourkova, Irina; Raschel, Kilian Reflected random walks and unstable Martin boundary. arXiv:2009.11596 Preprint, arXiv:2009.11596 [math.PR] (2020). BibTeX Cite \textit{I. Ignatiouk-Robert} et al., ``Reflected random walks and unstable Martin boundary'', Preprint, arXiv:2009.11596 [math.PR] (2020) Full Text: arXiv OA License
Bostan, Alin; Di Vizio, Lucia; Raschel, Kilian Differential transcendence of Bell numbers and relatives: a Galois theoretic approach. arXiv:2012.15292 Preprint, arXiv:2012.15292 [math.NT] (2020). BibTeX Cite \textit{A. Bostan} et al., ``Differential transcendence of Bell numbers and relatives: a Galois theoretic approach'', Preprint, arXiv:2012.15292 [math.NT] (2020) Full Text: arXiv OA License
Dreyfus, Thomas; Raschel, Kilian Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks. (English) Zbl 1468.12004 Actes de la conférence «Analogies between number field and function field : algebraic and analytic approaches ». Besançon: Presses Universitaires de Franche-Comté. Publ. Math. Besançon, Algèbre Théor. Nombres 2019, Part 1, 41-80 (2019). MSC: 12H10 39A06 05A15 30D05 PDFBibTeX XMLCite \textit{T. Dreyfus} and \textit{K. Raschel}, Publ. Math. Besançon, Algèbre Théor. Nombres 2019, 41--80 (2019; Zbl 1468.12004) Full Text: arXiv
Franceschi, Sandro; Raschel, Kilian Integral expression for the stationary distribution of reflected Brownian motion in a wedge. (English) Zbl 1428.62081 Bernoulli 25, No. 4B, 3673-3713 (2019). MSC: 60J65 60K25 PDFBibTeX XMLCite \textit{S. Franceschi} and \textit{K. Raschel}, Bernoulli 25, No. 4B, 3673--3713 (2019; Zbl 1428.62081) Full Text: DOI arXiv Euclid
Raschel, Kilian; Trotignon, Amélie On walks avoiding a quadrant. (English) Zbl 1418.05011 Electron. J. Comb. 26, No. 3, Research Paper P3.31, 34 p. (2019). MSC: 05A15 60K25 60C05 PDFBibTeX XMLCite \textit{K. Raschel} and \textit{A. Trotignon}, Electron. J. Comb. 26, No. 3, Research Paper P3.31, 34 p. (2019; Zbl 1418.05011) Full Text: arXiv Link
Bostan, Alin; Marynych, Alexander; Raschel, Kilian On the least common multiple of several random integers. (English) Zbl 1473.11155 J. Number Theory 204, 113-133 (2019). MSC: 11K65 11A05 11A25 11N37 60F05 PDFBibTeX XMLCite \textit{A. Bostan} et al., J. Number Theory 204, 113--133 (2019; Zbl 1473.11155) Full Text: DOI arXiv
Boutillier, Cédric; Tilière, Béatrice de; Raschel, Kilian The \(Z\)-invariant Ising model via dimers. (English) Zbl 1419.82008 Probab. Theory Relat. Fields 174, No. 1-2, 235-305 (2019). Reviewer: Hasan Akin (Gaziantep) MSC: 82B20 PDFBibTeX XMLCite \textit{C. Boutillier} et al., Probab. Theory Relat. Fields 174, No. 1--2, 235--305 (2019; Zbl 1419.82008) Full Text: DOI arXiv
Alsmeyer, Gerold; Raschel, Kilian The extinction problem for a distylous plant population with sporophytic self-incompatibility. (English) Zbl 1411.60105 J. Math. Biol. 78, No. 6, 1841-1874 (2019). MSC: 60J05 60H25 60K05 PDFBibTeX XMLCite \textit{G. Alsmeyer} and \textit{K. Raschel}, J. Math. Biol. 78, No. 6, 1841--1874 (2019; Zbl 1411.60105) Full Text: DOI arXiv
Bousquet-Mélou, Mireille; Fusy, Éric; Raschel, Kilian Plane bipolar orientations and quadrant walks. arXiv:1905.04256 Preprint, arXiv:1905.04256 [math.CO] (2019). MSC: 05A15 05A16 60G50 60F17 60G40 BibTeX Cite \textit{M. Bousquet-Mélou} et al., ``Plane bipolar orientations and quadrant walks'', Preprint, arXiv:1905.04256 [math.CO] (2019) Full Text: arXiv OA License
Franceschi, S.; Raschel, Kilian Tutte’s invariant approach for Brownian motion reflected in the quadrant. (English) Zbl 1393.60088 ESAIM, Probab. Stat. 21, 220-234 (2017). MSC: 60J65 60C05 60E10 PDFBibTeX XMLCite \textit{S. Franceschi} and \textit{K. Raschel}, ESAIM, Probab. Stat. 21, 220--234 (2017; Zbl 1393.60088) Full Text: DOI arXiv
Courtiel, J.; Melczer, S.; Mishna, M.; Raschel, K. Weighted lattice walks and universality classes. (English) Zbl 1369.05011 J. Comb. Theory, Ser. A 152, 255-302 (2017). MSC: 05A15 60G50 PDFBibTeX XMLCite \textit{J. Courtiel} et al., J. Comb. Theory, Ser. A 152, 255--302 (2017; Zbl 1369.05011) Full Text: DOI arXiv
Boutillier, Cédric; de Tilière, Béatrice; Raschel, Kilian The \(Z\)-invariant massive Laplacian on isoradial graphs. (English) Zbl 1372.82016 Invent. Math. 208, No. 1, 109-189 (2017). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 82B26 82B20 PDFBibTeX XMLCite \textit{C. Boutillier} et al., Invent. Math. 208, No. 1, 109--189 (2017; Zbl 1372.82016) Full Text: DOI arXiv
Bostan, A.; Kurkova, I.; Raschel, K. A human proof of Gessel’s lattice path conjecture. (English) Zbl 1350.05006 Trans. Am. Math. Soc. 369, No. 2, 1365-1393 (2017). MSC: 05A15 30F10 30D05 PDFBibTeX XMLCite \textit{A. Bostan} et al., Trans. Am. Math. Soc. 369, No. 2, 1365--1393 (2017; Zbl 1350.05006) Full Text: DOI arXiv
Franceschi, Sandro; Kurkova, Irina; Raschel, Kilian Analytic approach for reflected Brownian motion in the quadrant. (English) Zbl 1412.60118 Neininger, Ralph (ed.) et al., Proceedings of the 27th international conference on probabilistic, combinatorial and asymptotic methods for the analysis of algorithms – AofA’16, Kraków, Poland, July 4–8, 2016. Kraków: Jagiellonian University, Department of Theoretical Computer Science. 19 p. (2016). MSC: 60J65 60G50 PDFBibTeX XMLCite \textit{S. Franceschi} et al., in: Proceedings of the 27th international conference on probabilistic, combinatorial and asymptotic methods for the analysis of algorithms -- AofA'16, Kraków, Poland, July 4--8, 2016. Kraków: Jagiellonian University, Department of Theoretical Computer Science. 19 p. (2016; Zbl 1412.60118) Full Text: arXiv
Lecouvey, Cédric; Raschel, Kilian \(t\)-Martin boundary of killed random walks in the quadrant. (English) Zbl 1367.60048 Donati-Martin, Catherine (ed.) et al., Séminaire de probabilités XLVIII. Cham: Springer (ISBN 978-3-319-44464-2/pbk; 978-3-319-44465-9/ebook). Lecture Notes in Mathematics 2168. Séminaire de Probabilités, 305-323 (2016). MSC: 60G50 31C35 60J50 31A05 05A15 PDFBibTeX XMLCite \textit{C. Lecouvey} and \textit{K. Raschel}, Lect. Notes Math. 2168, 305--323 (2016; Zbl 1367.60048) Full Text: DOI arXiv
Garbit, Rodolphe; Raschel, Kilian On the exit time from a cone for random walks with drift. (English) Zbl 1346.60060 Rev. Mat. Iberoam. 32, No. 2, 511-532 (2016). Reviewer: Aleksander Iksanov (Kiev) MSC: 60G50 60F99 05A16 PDFBibTeX XMLCite \textit{R. Garbit} and \textit{K. Raschel}, Rev. Mat. Iberoam. 32, No. 2, 511--532 (2016; Zbl 1346.60060) Full Text: DOI arXiv
Kurkova, Irina; Raschel, Kilian New steps in walks with small steps in the quarter plane: series expressions for the generating functions. (English) Zbl 1326.05010 Ann. Comb. 19, No. 3, 461-511 (2015). MSC: 05A15 30F10 30D05 PDFBibTeX XMLCite \textit{I. Kurkova} and \textit{K. Raschel}, Ann. Comb. 19, No. 3, 461--511 (2015; Zbl 1326.05010) Full Text: DOI arXiv
Fayolle, Guy; Raschel, Kilian About a possible analytic approach for walks in the quarter plane with arbitrary big jumps. (Autour d’une approche analytique pour les marches à sauts arbitrairement grands dans le quart de plan.) (English. French summary) Zbl 1319.60090 C. R., Math., Acad. Sci. Paris 353, No. 2, 89-94 (2015). MSC: 60G50 35Q15 30F10 PDFBibTeX XMLCite \textit{G. Fayolle} and \textit{K. Raschel}, C. R., Math., Acad. Sci. Paris 353, No. 2, 89--94 (2015; Zbl 1319.60090) Full Text: DOI arXiv HAL
Raschel, Kilian Walks in the quarter plane: analytic approach and applications. (English) Zbl 1334.60073 ESAIM, Proc. 44, 140-149 (2014). MSC: 60G50 92D25 PDFBibTeX XMLCite \textit{K. Raschel}, ESAIM, Proc. 44, 140--149 (2014; Zbl 1334.60073) Full Text: DOI
Garbit, Rodolphe; Raschel, Kilian On the exit time from a cone for Brownian motion with drift. (English) Zbl 1317.60104 Electron. J. Probab. 19, Paper No. 63, 27 p. (2014). MSC: 60J65 60G50 60F17 60J05 PDFBibTeX XMLCite \textit{R. Garbit} and \textit{K. Raschel}, Electron. J. Probab. 19, Paper No. 63, 27 p. (2014; Zbl 1317.60104) Full Text: DOI arXiv
Raschel, Kilian Random walks in the quarter plane, discrete harmonic functions and conformal mappings. (English) Zbl 1300.60066 Stochastic Processes Appl. 124, No. 10, 3147-3178 (2014). MSC: 60G50 31A05 31C35 60G40 39A12 PDFBibTeX XMLCite \textit{K. Raschel}, Stochastic Processes Appl. 124, No. 10, 3147--3178 (2014; Zbl 1300.60066) Full Text: DOI arXiv
Bostan, Alin; Raschel, Kilian; Salvy, Bruno Non-D-finite excursions in the quarter plane. (English) Zbl 1279.05003 J. Comb. Theory, Ser. A 121, 45-63 (2014). MSC: 05A15 60G50 PDFBibTeX XMLCite \textit{A. Bostan} et al., J. Comb. Theory, Ser. A 121, 45--63 (2014; Zbl 1279.05003) Full Text: DOI arXiv
Essifi, Rim; Peigné, Marc; Raschel, Kilian Some aspects of fluctuations of random walks on \(\mathbb R\) and applications to random walks on \(\mathbb R^+\) with non-elastic reflection at 0. (English) Zbl 1287.60056 ALEA, Lat. Am. J. Probab. Math. Stat. 10, No. 2, 591-607 (2013). MSC: 60G50 60F05 31C05 PDFBibTeX XMLCite \textit{R. Essifi} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 10, No. 2, 591--607 (2013; Zbl 1287.60056) Full Text: arXiv Link
Lafitte-Godillon, Pauline; Raschel, Kilian; Tran, Viet Chi Extinction probabilities for a distylous plant population modeled by an inhomogeneous random walk on the positive quadrant. (English) Zbl 1412.92203 SIAM J. Appl. Math. 73, No. 2, 700-722 (2013). MSC: 92D10 92C80 PDFBibTeX XMLCite \textit{P. Lafitte-Godillon} et al., SIAM J. Appl. Math. 73, No. 2, 700--722 (2013; Zbl 1412.92203) Full Text: DOI arXiv
Kurkova, Irina; Raschel, Kilian Passage time from four to two blocks of opinions in the voter model and walks in the quarter plane. (English) Zbl 1266.82040 Queueing Syst. 74, No. 2-3, 219-234 (2013). MSC: 82C22 60G50 60G40 30E20 PDFBibTeX XMLCite \textit{I. Kurkova} and \textit{K. Raschel}, Queueing Syst. 74, No. 2--3, 219--234 (2013; Zbl 1266.82040) Full Text: DOI arXiv
van Leeuwaarden, Johan S. H.; Raschel, Kilian Random walks reaching against all odds the other side of the quarter plane. (English) Zbl 1271.60059 J. Appl. Probab. 50, No. 1, 85-102 (2013). Reviewer: Robert I. A. Patterson (Berlin) MSC: 60G50 30E20 PDFBibTeX XMLCite \textit{J. S. H. van Leeuwaarden} and \textit{K. Raschel}, J. Appl. Probab. 50, No. 1, 85--102 (2013; Zbl 1271.60059) Full Text: DOI arXiv Euclid
Adan, Ivo J. B. F.; Van Leeuwaarden, Johan S. H.; Raschel, Kilian The compensation approach for walks with small steps in the quarter plane. (English) Zbl 1260.05005 Comb. Probab. Comput. 22, No. 2, 161-183 (2013). MSC: 05A15 05A16 PDFBibTeX XMLCite \textit{I. J. B. F. Adan} et al., Comb. Probab. Comput. 22, No. 2, 161--183 (2013; Zbl 1260.05005) Full Text: DOI arXiv
Rasche, Kilian Paths confined within a quadrant. (Chemins confinés dans un quadrant.) (French) Zbl 1365.05267 Matapli 99, 49-56 (2012). MSC: 05C81 05A15 PDFBibTeX XMLCite \textit{K. Rasche}, Matapli 99, 49--56 (2012; Zbl 1365.05267)
Fayolle, Guy; Raschel, Kilian Some exact asymptotics in the counting of walks in the quarter plane. (English) Zbl 1296.60111 Broutin, Nicolas (ed.) et al., Proceeding of the 23rd international meeting on probabilistic, combinatorial, and asymptotic methods in the analysis of algorithms (AofA’12), Montreal, Canada, June 18–22, 2012. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 109-124, electronic only (2012). MSC: 60G50 05A16 30D05 30F10 PDFBibTeX XMLCite \textit{G. Fayolle} and \textit{K. Raschel}, in: Proceeding of the 23rd international meeting on probabilistic, combinatorial, and asymptotic methods in the analysis of algorithms (AofA'12), Montreal, Canada, June 18--22, 2012. Nancy: The Association. Discrete Mathematics \& Theoretical Computer Science (DMTCS). 109--124 (2012; Zbl 1296.60111) Full Text: arXiv Link
Kurkova, Irina; Raschel, Kilian On the functions counting walks with small steps in the quarter plane. (English) Zbl 1255.05012 Publ. Math., Inst. Hautes Étud. Sci. 116, 69-114 (2012). MSC: 05A15 PDFBibTeX XMLCite \textit{I. Kurkova} and \textit{K. Raschel}, Publ. Math., Inst. Hautes Étud. Sci. 116, 69--114 (2012; Zbl 1255.05012) Full Text: DOI arXiv
Raschel, Kilian Counting walks in a quadrant: a unified approach via boundary value problems. (English) Zbl 1238.05014 J. Eur. Math. Soc. (JEMS) 14, No. 3, 749-777 (2012). MSC: 05A15 30F10 30D05 60G50 PDFBibTeX XMLCite \textit{K. Raschel}, J. Eur. Math. Soc. (JEMS) 14, No. 3, 749--777 (2012; Zbl 1238.05014) Full Text: DOI arXiv Backlinks: MO
Raschel, Kilian Green functions for killed random walks in the Weyl chamber of \(\mathrm{Sp}(4)\). (English. French summary) Zbl 1263.60043 Ann. Inst. Henri Poincaré, Probab. Stat. 47, No. 4, 1001-1019 (2011). MSC: 60G50 31C35 30E20 30F10 PDFBibTeX XMLCite \textit{K. Raschel}, Ann. Inst. Henri Poincaré, Probab. Stat. 47, No. 4, 1001--1019 (2011; Zbl 1263.60043) Full Text: DOI arXiv Euclid
Fayolle, G.; Raschel, K. Random walks in the quarter-plane with zero drift: an explicit criterion for the finiteness of the associated group. (English) Zbl 1263.60039 Markov Process. Relat. Fields 17, No. 4, 619-636 (2011). Reviewer: Ilie Valuşescu (Bucureşti) MSC: 60G50 30F10 30D05 PDFBibTeX XMLCite \textit{G. Fayolle} and \textit{K. Raschel}, Markov Process. Relat. Fields 17, No. 4, 619--636 (2011; Zbl 1263.60039) Full Text: arXiv
Kurkova, Irina; Raschel, Kilian Random walks in \((\mathbb Z_+)^2\) with non-zero drift absorbed at the axes. (English. French summary) Zbl 1243.60042 Bull. Soc. Math. Fr. 139, No. 3, 341-387 (2011). Reviewer: Ilie Valuşescu (Bucureşti) MSC: 60G50 60G40 30E20 30F10 PDFBibTeX XMLCite \textit{I. Kurkova} and \textit{K. Raschel}, Bull. Soc. Math. Fr. 139, No. 3, 341--387 (2011; Zbl 1243.60042) Full Text: DOI arXiv Link
Kurkova, Irina; Raschel, Kilian Explicit expression for the generating function counting Gessel’s walks. (English) Zbl 1234.05027 Adv. Appl. Math. 47, No. 3, 414-433 (2011). MSC: 05A15 30F10 30D05 PDFBibTeX XMLCite \textit{I. Kurkova} and \textit{K. Raschel}, Adv. Appl. Math. 47, No. 3, 414--433 (2011; Zbl 1234.05027) Full Text: DOI arXiv
Fayolle, G.; Raschel, K. On the holonomy or algebraicity of generating functions counting lattice walks in the quarter-plane. (English) Zbl 1284.05018 Markov Process. Relat. Fields 16, No. 3, 485-496 (2010). MSC: 05A15 30F10 30D05 PDFBibTeX XMLCite \textit{G. Fayolle} and \textit{K. Raschel}, Markov Process. Relat. Fields 16, No. 3, 485--496 (2010; Zbl 1284.05018) Full Text: arXiv
Raschel, Kilian Green functions and Martin compactification for killed random walks related to \(SU(3)\). (English) Zbl 1226.60068 Electron. Commun. Probab. 15, 176-190 (2010). MSC: 60G50 31C35 30F10 PDFBibTeX XMLCite \textit{K. Raschel}, Electron. Commun. Probab. 15, 176--190 (2010; Zbl 1226.60068) Full Text: DOI arXiv EMIS
Raschel, Kilian Random Walks in the Quarter Plane Absorbed at the Boundary : Exact and Asymptotic. arXiv:0902.2785 Preprint, arXiv:0902.2785 [math.PR] (2009). MSC: 60G50 60G40 31C35 30E20 30E25 BibTeX Cite \textit{K. Raschel}, ``Random Walks in the Quarter Plane Absorbed at the Boundary : Exact and Asymptotic'', Preprint, arXiv:0902.2785 [math.PR] (2009) Full Text: arXiv OA License