A. Ancona, Principe de Harnack ?? la fronti??re et th??or??me de Fatou pour un op??rateur elliptique dans un domaine lipschitzien, Annales de l???institut Fourier, vol.28, issue.4, pp.169-213, 1978.
DOI : 10.5802/aif.720

S. Aspandiiarov, R. Iasnogorodski, and M. Menshikov, Passage-time moments for nonnegative stochastic processes and an application to reflected random walks in a quadrant, The Annals of Probability, vol.24, issue.2, pp.932-960, 1996.
DOI : 10.1214/aop/1039639371

P. Biane, Quantum random walk on the dual of SU(n). Probab. Theory Related Fields, pp.117-129, 1991.

P. Biane, Minuscule weights and random walks on lattices In Quantum probability & related topics, World Sci. Publ., River Edge NJ, pp.51-65, 1992.

M. Bousquet-mélou and M. Mishna, Walks with small steps in the quarter plane, Contemp. Math, vol.520, pp.1-40, 2010.
DOI : 10.1090/conm/520/10252

J. W. Cohen and O. J. Boxma, Boundary value problems in queueing system analysis, 1983.

D. Denisov and V. Wachtel, Conditional Limit Theorems for Ordered Random Walks, Electronic Journal of Probability, vol.15, issue.0, pp.292-322, 2010.
DOI : 10.1214/EJP.v15-752

D. Denisov and V. Wachtel, Random walks in cones, The Annals of Probability, vol.43, issue.3, 2014.
DOI : 10.1214/13-AOP867

E. Dynkin, The boundary theory of Markov processes (discrete case) Uspehi Mat, Nauk, vol.24, pp.3-42, 1969.

F. Dyson, A Brownian???Motion Model for the Eigenvalues of a Random Matrix, Journal of Mathematical Physics, vol.3, issue.6, pp.1191-1198, 1962.
DOI : 10.1063/1.1703862

P. Eichelsbacher and W. König, Ordered Random Walks, Electronic Journal of Probability, vol.13, issue.0, pp.1307-1336, 2008.
DOI : 10.1214/EJP.v13-539

G. Fayolle and R. Iasnogorodski, Two coupled processors: The reduction to a Riemann-Hilbert problem, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.13, issue.No. 6, pp.325-351, 1979.
DOI : 10.1007/BF00535168

G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the quarter plane, 1999.
URL : https://hal.archives-ouvertes.fr/inria-00572276

G. Fayolle and K. , On the holonomy or algebraicity of generating functions counting lattice walks in the quarter plane. Markov Process, pp.485-496, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00559676

G. Fayolle and K. , Random walks in the quarter-plane with zero drift: an explicit criterion for the finiteness of the associated group. Markov Process, pp.619-636, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00572276

I. Ignatiouk-robert, Martin Boundary of a Killed Random Walk on a Half-Space, Journal of Theoretical Probability, vol.121, issue.4, pp.35-68, 2008.
DOI : 10.1007/s10959-007-0100-3

I. Ignatiouk-robert, Martin boundary of a killed random walk on Z d . Preprint arXiv:0909, pp.1-49, 2009.

I. Ignatiouk-robert, Martin boundary of a reflected random walk on a half-space, Probability Theory and Related Fields, vol.121, issue.1, pp.197-245, 2010.
DOI : 10.1007/s00440-009-0228-4

I. Ignatiouk-robert and C. Loree, Martin boundary of a killed random walk on a quadrant, The Annals of Probability, vol.38, issue.3, pp.1106-1142, 2010.
DOI : 10.1214/09-AOP506

W. König and P. Schmid, Random walks conditioned to stay in Weyl chambers of type C and D, Electronic Communications in Probability, vol.15, issue.0, pp.286-296, 2010.
DOI : 10.1214/ECP.v15-1560

I. Kurkova and K. , Random walks in $(\mathbb{Z}_{+})^{2}$ with non-zero drift absorbed at the axes, Bulletin de la Société mathématique de France, vol.139, issue.3, pp.341-387, 2011.
DOI : 10.24033/bsmf.2611
URL : https://hal.archives-ouvertes.fr/hal-00696352

G. Litvinchuk, Solvability theory of boundary value problems and singular integral equations with shift, 2000.
DOI : 10.1007/978-94-011-4363-9

V. Malyshev, Positive random walks and Galois theory, Uspehi Mat. Nauk, vol.26, pp.227-228, 1971.

M. Picardello, W. Woess, and W. , Martin boundaries of cartesian products of markov chains, Nagoya Mathematical Journal, vol.33, issue.51, pp.153-169, 1992.
DOI : 10.1214/aoms/1177700401

R. T. Rockafellar, Convex analysis, 1972.
DOI : 10.1515/9781400873173

G. Sansone and J. Gerretsen, Lectures on the theory of functions of a complex variable. I. Holomorphic functions, Noordhoff, 1960.

N. T. Varopoulos, Potential theory in conical domains, Mathematical Proceedings of the Cambridge Philosophical Society, vol.125, issue.2, pp.335-384, 1999.
DOI : 10.1017/S0305004198002771

N. T. Varopoulos, Potential theory in conical domains. II, Mathematical Proceedings of the Cambridge Philosophical Society, vol.129, issue.2, pp.301-319, 2000.
DOI : 10.1017/S0305004100004503

N. T. Varopoulos, Potential theory in conical domains (III), Mathematical Proceedings of the Cambridge Philosophical Society, vol.131, issue.02, pp.327-361, 2001.
DOI : 10.1017/S0305004101004972

N. T. Varopoulos, The Discrete and Classical Dirichlet Problem, Milan Journal of Mathematics, vol.21, issue.2, pp.397-436, 2009.
DOI : 10.1007/s00032-009-0109-4

W. Woess, Random walks and discrete potential theory, 1999.