G. Anderson, A. Guionnet, and O. , Zeitouni An Introduction to Random Matrices. Cambridge studies in advanced mathematics, p.118, 2009.

P. Biane, P. Bougerol, and N. O. , Connell Littelmann paths and Brownian paths, Duke Math, J, vol.130, pp.127-167, 2005.

P. Bougerol and T. , Jeulin Paths in Weyl chambers and random matrices Probab, Probability Theory and Related Fields, vol.124, issue.4, pp.517-543, 2002.
DOI : 10.1007/s004400200221

G. P. Chistyakov and F. , Götze Distribution of the shape of Markovian random words, pp.18-36, 2004.

P. Glynn and W. , Departures from Many Queues in Series, The Annals of Applied Probability, vol.1, issue.4, pp.546-572, 1991.
DOI : 10.1214/aoap/1177005838

J. Gravner, C. A. Tracy, and H. , Widom Limit theorems for height fluctuations in a class of discrete space and time growth models, Journal of Statistical Physics, vol.102, issue.5/6, pp.1085-1132, 2001.
DOI : 10.1023/A:1004879725949

C. Houdré and T. , Litherland On the longest increasing subsequence for finite and countable alphabets, in High Dimensional Probability V: The Luminy Volume, pp.185-212, 2009.

C. Houdré and T. , Litherland On the limiting shape of Young diagrams associated with Markov random words, 2011.

C. Houdré and T. Litherland, Asymptotics for the Length of the Longest Increasing Subsequence of a Binary Markov Random Word, Proceedings in Mathematics & Statistics, pp.511-524, 2013.
DOI : 10.1007/978-1-4614-5906-4_23

C. Houdré and H. , Xu On the limiting shape of Young diagrams associated with inhomogeneous random words, in: High Dimensional Probability VI: The Banff volume Progress in Probability, p.Birkhauser, 2013.

A. Its, C. A. Tracy, and H. , Widom Random words, Toeplitz determinants, and integrable systems. I. Random matrix models and their applications, Math. Sci. Res. Inst. Publ, vol.40, pp.245-258, 2001.
DOI : 10.1016/s0167-2789(01)00171-3

URL : http://arxiv.org/abs/nlin/0004018

A. Its, C. A. Tracy, and H. , Widom Random words, Toeplitz determinants, and integrable systems. II Advances in nonlinear mathematics and science, Phys. D, vol.152, pp.153-199, 2001.
DOI : 10.1016/s0167-2789(01)00171-3

URL : http://arxiv.org/abs/nlin/0004018

K. Johansson and E. , Eigenvalues of GUE Minors, Paper no. 50, pp.1342-1371, 2006.
DOI : 10.1214/EJP.v11-370

S. Kerov, Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis, AMS, Translations of Mathematical Monographs, vol.219, 1994.

G. Kuperberg, Random words, quantum statistics, central limits, random matrices, Methods and Applications of Analysis, vol.9, issue.1, pp.99-118, 2002.
DOI : 10.4310/MAA.2002.v9.n1.a3

N. O. Connell and M. , A Representation for Non-Colliding Random Walks, Electronic Communications in Probability, vol.7, issue.0, pp.1-12, 2002.
DOI : 10.1214/ECP.v7-1042

C. Tracy and H. , On the distributions of the lengths of the longest monotone subsequences in random words, Probability Theory and Related Fields, vol.119, issue.3, pp.350-380, 2001.
DOI : 10.1007/PL00008763