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Some examples of dynamics for GelfandTsetlin patterns
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Warren, Jon and Windridge, Peter. (2009) Some examples of dynamics for GelfandTsetlin patterns. Electronic Journal of Probability, Vol.14 . pp. 17451769. ISSN 10836489

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Abstract
We give three examples of stochastic processes in the GelfandTsetlin cone in which each component evolves independently apart from a blocking and pushing interaction. These processes give rise to couplings between certain conditioned Markov processes, last passage times and exclusion processes. In the first two examples, we deduce known identities in distribution between such processes whilst in the third example, the components of the process cannot escape past a wall at the origin and we obtain a new relation.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Stochastic processes 
Journal or Publication Title:  Electronic Journal of Probability 
Publisher:  University of Washington. Dept. of Mathematics 
ISSN:  10836489 
Date:  2009 
Volume:  Vol.14 
Number of Pages:  25 
Page Range:  pp. 17451769 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Open Access 
References:  [1] J. Baik, P. Deift, and K. Johansson. On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc., 12(4):1119–1178, 1999. MR1682248 [2] Y. Baryshnikov. GUEs and queues. Probab. Theory Related Fields, 119(2):256–274, 2001. MR1818248 [3] A. Borodin and P. L. Ferrari. Anisotropic growth of random surfaces in 2+ 1 dimensions. arXiv:0804.3035. [4] A. Borodin and P. L. Ferrari. Large time asymptotics of growth models on spacelike paths. I. PushASEP. Electron. J. Probab., 13:no. 50, 1380–1418, 2008. MR2438811 [5] A. Borodin, P. L. Ferrari, M. Prähofer, T. Sasamoto, and J. Warren. Maximum of Dyson Brownian motion and noncolliding systems with a boundary. arXiv:0905.3989. [6] A. Borodin, P. L. Ferrari, and T. Sasamoto. Large time asymptotics of growth models on spacelike paths. II. PNG and parallel TASEP. Comm. Math. Phys., 283(2):417–449, 2008. MR2430639 [7] M. Defosseux. Orbit measures and interlaced determinantal point processes. C. R. Math. Acad. Sci. Paris, 346(1314):783–788, 2008. MR2427082 [8] A. Dieker and J. Warren. On the LargestEigenvalue Process For Generalized Wishart Random Matrices. arXiv:0812.1504. [9] M. Fulmek and C. Krattenthaler. Lattice path proofs for determinantal formulas for symplectic and orthogonal characters. J. Combin. Theory Ser. A, 77(1):3–50, 1997. MR1426737 [10] W. Fulton. Young tableaux, volume 35 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 1997. With applications to representation theory and geometry. MR1464693 [11] Y. V. Fyodorov. Introduction to the random matrix theory: Gaussian unitary ensemble and beyond. In Recent perspectives in random matrix theory and number theory, volume 322 of London Math. Soc. Lecture Note Ser., pages 31–78. Cambridge Univ. Press, Cambridge, 2005. MR2166458 [12] K. Johansson. A multidimensional Markov chain and the Meixner ensemble. arXiv:0707.0098. [13] K. Johansson. Shape fluctuations and random matrices. Comm. Math. Phys., 209(2):437–476, 2000. MR1737991 [14] K. Johansson. Nonintersecting paths, random tilings and random matrices. Probab. Theory Related Fields, 123(2):225–280, 2002. MR1900323 [15] K. Johansson. Discrete polynuclear growth and determinantal processes. Comm. Math. Phys., 242(12):277–329, 2003. MR2018275 [16] K. Johansson. Random Matrices and determinantal processes. In Lecture Notes of the Les Houches Summer School 2005. Elselvier, 2005. [17] W. König, N. O’Connell, and S. Roch. Noncolliding random walks, tandem queues, and discrete orthogonal polynomial ensembles. Electron. J. Probab., 7:no. 5, 24 pp. (electronic), 2002. MR1887625 [18] M. Maliakas. On odd symplectic Schur functions. J. Algebra, 211(2):640–646, 1999. MR1666663 [19] E. Nordenstam. On the shuffling algorithm for domino tilings. arXiv:0802.2592. [20] N. O’Connell. Conditioned random walks and the RSK correspondence. J. Phys. A, 36(12):3049–3066, 2003. Random matrix theory. MR1986407 [21] N. O’Connell and M. Yor. A representation for noncolliding random walks. Electron. Comm. Probab., 7:1–12 (electronic), 2002. MR1887169 [22] M. Prähofer and H. Spohn. Scale invariance of the PNG droplet and the Airy process. J. Statist. Phys., 108(56):1071–1106, 2002. Dedicated to David Ruelle and Yasha Sinai on the occasion of their 65th birthdays. MR1933446 [23] R. A. Proctor. Odd symplectic groups. Invent. Math., 92(2):307–332, 1988. MR0936084 [24] L. C. G. Rogers and J. W. Pitman. Markov functions. Ann. Probab., 9(4):573–582, 1981. MR0624684 [25] T. Sasamoto. Fluctuations of the onedimensional asymmetric exclusion process using random matrix techniques. J. Stat. Mech. Theory Exp., (7):P07007, 31 pp. (electronic), 2007. MR2335692 [26] S. Sundaram. Tableaux in the representation theory of the classical Lie groups. In Invariant theory and tableaux (Minneapolis, MN, 1988), volume 19 of IMA Vol. Math. Appl., pages 191– 225. Springer, New York, 1990. MR1035496 [27] B. Tóth and B. Vet˝o. Skorohodreflection of Brownian paths and BES3. Acta Sci. Math. (Szeged), 73(34):781–788, 2007. MR2380076 [28] C. A. Tracy and H. Widom. Levelspacing distributions and the Airy kernel. Comm. Math. Phys., 159(1):151–174, 1994. MR1257246 [29] J.Warren. Dyson’s Brownian motions, intertwining and interlacing. Electron. J. Probab., 12:no. 19, 573–590 (electronic), 2007. MR2299928 
URI:  http://wrap.warwick.ac.uk/id/eprint/17394 
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