R. Bañuelos and R. Smits, Brownian motion in cones, Probability Theory and Related Fields, vol.108, issue.3, pp.299-319, 1997.
DOI : 10.1007/s004400050111

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, Quantum probability & related topics, pp.51-65, 1992.
DOI : 10.1142/9789814354783_0004

P. Biane, P. Bougerol, O. Connell, and N. , Littelmann paths and Brownian paths, Duke Mathematical Journal, vol.130, issue.1, pp.127-167, 2005.
DOI : 10.1215/S0012-7094-05-13014-9

URL : https://hal.archives-ouvertes.fr/hal-00018663

P. Billingsley, Convergence of probability measures, 1968.
DOI : 10.1002/9780470316962

M. Bousquet-mélou and M. Mishna, Walks with small steps in the quarter plane, Algorithmic probability and combinatorics, pp.1-39, 2010.
DOI : 10.1090/conm/520/10252

R. D. Deblassie, Exit times from cones in ??? n of Brownian motion, Probability Theory and Related Fields, vol.26, issue.1, pp.1-29, 1987.
DOI : 10.1007/BF01845637

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

URL : http://arxiv.org/abs/0907.2854

D. Denisov and W. Wachtel, Random walks in cones, The Annals of Probability, vol.43, issue.3, p.43, 2015.
DOI : 10.1214/13-AOP867

R. A. Doney, On the asymptotic behaviour of first passage times for transient random walk, Probability Theory and Related Fields, vol.10, issue.2, pp.239-246, 1989.
DOI : 10.1007/BF00319553

Y. Doumerc, O. Connell, and N. , Exit problems associated with finite reflection groups, Probability Theory and Related Fields, vol.83, issue.4, pp.501-538, 2005.
DOI : 10.1007/s00440-004-0402-7

J. Duraj, Random walks in cones: The case of nonzero drift. Stochastic Process, Appl, vol.124, pp.1503-1518, 2014.

D. 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 K. Raschel, Some exact asymptotics in the counting of walks in the quarter plane, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), Discrete Math. Theor. Comput. Sci. Proc., AQ, pp.109-124, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00661541

R. Garbit, Temps de sortie d'un c??ne pour une marche al??atoire centr??e, Comptes Rendus Mathematique, vol.345, issue.10, pp.587-591, 2007.
DOI : 10.1016/j.crma.2007.10.016

R. Garbit and K. Raschel, On the exit time from a cone for brownian motion with drift, Electronic Journal of Probability, vol.19, issue.0, pp.1-27, 2014.
DOI : 10.1214/EJP.v19-3169

URL : https://hal.archives-ouvertes.fr/hal-00880523

D. Iglehart, Random walks with negative drift conditioned to stay positive, Journal of Applied Probability, vol.234, issue.04, pp.742-751, 1974.
DOI : 10.1007/BF02795339

S. Johnson, M. Mishna, and K. Yeats, Towards a combinatorial understanding of lattice path asymptotics, 2013.

Z. Pucha-la and T. Rolski, The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts, Probability Theory and Related Fields, vol.10, issue.3-4, pp.595-617, 2008.
DOI : 10.1007/s00440-007-0116-8

R. Rockafellar, Convex analysis, 1970.
DOI : 10.1515/9781400873173

F. Spitzer, Principles of random walk. The University Series in Higher Mathematics, 1964.

N. 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

B. Lavoisier, 49045 Angers Cedex 1, France E-mail address: rodolphe.garbit@univ-angers.fr CNRS, Fédération Denis Poisson