Random matrices, non-colliding processes and queues
O'Connell, Neil
Séminaire de probabilités de Strasbourg, Tome 36 (2002), p. 165-182 / Harvested from Numdam
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@article{SPS_2002__36__165_0,
     author = {O'Connell, Neil},
     title = {Random matrices, non-colliding processes and queues},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {36},
     year = {2002},
     pages = {165-182},
     mrnumber = {1971584},
     zbl = {1041.15019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/SPS_2002__36__165_0}
}

O'Connell, Neil. Random matrices, non-colliding processes and queues. Séminaire de probabilités de Strasbourg, Tome 36 (2002) pp. 165-182. http://gdmltest.u-ga.fr/item/SPS_2002__36__165_0/

[1] F. Baccelli, A. Borovkov and J. Mairesse. Asymptotic results on infinite tandem queueing networks. Probab. Theor. Rel. Fields 118, n. 3, p. 365-405, 2000. | MR 1800538 | Zbl 0976.60088

[2] F. Baccelli, G. Cohen, G.J. Olsder and J.-P. Quadrat. Synchronization and Linearity : An Algebra for Discrete Event Systems. Wiley, 1992. | MR 1204266 | Zbl 0824.93003

[3] J. Baik. Random vicious walks and random matrices. Comm. Pure Appl. Math. 53 (2000) 1385-1410. | MR 1773413 | Zbl 1026.60071

[4] 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 (1999), no. 4,1119-1178. | MR 1682248 | Zbl 0932.05001

[5] Yu. Baryshnikov. GUES and queues. Probab. Theor. Rel. Fields 119 (2001) 256-274. | MR 1818248 | Zbl 0980.60042

[6] Ph. Biane. Quelques propriétés du mouvement brownien dans un cone. Stoch. Proc. Appl. 53 (1994), no. 2, 233-240. | MR 1302912 | Zbl 0812.60067

[7] Ph. Biane. Théorème de Ney-Spitzer sur le dual de SU(2). Trans. Amer. Math. Soc. 345, no. 1 (1994) 179-194. | MR 1225572 | Zbl 0814.60064

[8] Ph. Bougerol and Th. Jeulin. Paths in Weyl chambers and random matrices. Preprint. | MR 1942321

[9] P. Brémaud. Point Processes and Queues: Martingale Dynamics. Springer-Verlag, Berlin, 1981. | MR 636252 | Zbl 0478.60004

[10] P. Brémaud. Markov Chains, Gibbs Fields, Monte-Carlo Simulation, and Queues. Texts in App. Maths., vol. 31. Springer, 1999. | MR 1689633 | Zbl 0949.60009

[11] P.J. Burke. The output of a queueing system. Operations Research 4 (1956), no. 6, 699-704. | MR 83416

[12] Ph. Carmona, F. Petit and M. Yor. Exponential functionals of Lévy processes. In: Lévy Processes: Theory and Applications, eds. O. Barndorff-Nielsen, T. Mikosch and S. Resnick. Birkhäuser, 2001. | MR 1833691 | Zbl 0979.60038

[13] Ph. Carmona, F. Petit and M. Yor. An identity in law involving reflecting Brownian motion, derived for generalized arc-sine laws for perturbed Brownian motions. Stoch. Proc. Appl. (1999) 323-334. | MR 1671824 | Zbl 0965.60074

[14] E. Cépa and D. Lépingle. Diffusing particles with electrostatic repulsion. Probab. Th. Rel. Fields 107 (1997), no. 4, 429-449. | MR 1440140 | Zbl 0883.60089

[15] J.W. Cohen. On the queueing process of lanes. Internal report Philips Telecommunicatie Industrie, Hilversum (NL). October 2, 1956.

[16] B. Derrida. Directed polymers in a random medium. Physica A 163 (1990) 71-84. | MR 1043640

[17] C. Donati-Martin, H. Matsumoto and M. Yor. Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions. Pub. RIMS, Kyoto, vol. 37, no. 3, p295-326. | MR 1855425 | Zbl 1033.60085

[18] C. Donati-Martin, H. Matsumoto and M. Yor. The law of geometric Brownian motion and its integral, revisited; application to conditional moments. To appear in the Proceedings of the First Bachelier Conference, Springer, 2001. | MR 1960566 | Zbl 1030.91029

[19] D. Dufresne. An affine property of the reciprocal Asian option process. Osaka Math J. 38 (2001) 17-20. | MR 1833627 | Zbl 0987.60026

[20] D. Dufresne. The integral of geometric Brownian motion Adv. Appl. Probab. 33(1), (2001) 223-241. | MR 1825324 | Zbl 0980.60103

[21] F.J. Dyson. A Brownian-motion model for the eigenvalues of a random matrix. J. Math. Phys. 3 (1962) 1191-1198. | MR 148397 | Zbl 0111.32703

[22] P.J. Forrester. Random walks and random permutations. Preprint, 1999. (XXX: math.CO/9907037) | MR 1752728

[23] A.J. Ganesh. Large deviations of the sojourn time for queues in series. Ann. Oper. Res. 79:3-26, 1998. | MR 1630872 | Zbl 0896.90095

[24] P.W. Glynn and W. Whitt. Departures from many queues in series. Ann. Appl. Prob. 1 (1991), no. 4, 546-572. | MR 1129774 | Zbl 0749.60090

[25] D. Grabiner. Brownian motion in a Weyl chamber, non-colliding particles, and random matrices. Ann. IHP 35 (1999), no. 2, 177-204. | Numdam | MR 1678525 | Zbl 0937.60075

[26] J. Gravner, C.A. Tracy and H. Widom. Limit theorems for height fluctuations in a class of discrete space and time growth models. J. Stat. Phys. 102 (2001), nos. 5-6, 1085-1132. | MR 1830441 | Zbl 0989.82030

[27] B.M. Hambly, James Martin and Neil O'Connell. Concentration results for a Brownian directed percolation problem. Preprint. | MR 1935124

[28] B.M. Hambly, James Martin and Neil O'Connell. Pitman's 2M - X theorem for skip-free random walks with Markovian increments. Elect. Commun. Probab., Vol. 6 (2001) Paper no. 7, pages 73-77. | MR 1855343 | Zbl 0985.60070

[29] J.M. Harrison and R.J. Williams. On the quasireversibility of a multiclass Brownian service station. Ann. Probab. 18 (1990) 1249-1268. | MR 1062068 | Zbl 0709.60081

[30] D. Hobson and W. Werner. Non-colliding Brownian motion on the circle, Bull. Math. Soc. 28 (1996) 643-650. | MR 1405497 | Zbl 0853.60060

[31] K. Johansson. Shape fluctuations and random matrices. Commun. Math. Phys. 209 (2000) 437-476. | MR 1737991 | Zbl 0969.15008

[32] K. Johansson. Discrete orthogonal polynomial ensembles and the Plancherel measure, Ann. Math. (2) 153 (2001), no. 1, 259-296. | MR 1826414 | Zbl 0984.15020

[33] I.M. Johnstone. On the distribution of the largest principal component. Ann. Stat. 29, No. 2 (2001). | MR 1863961 | Zbl 1016.62078

[34] F.P. Kelly. Reversibility and Stochastic Networks. Wiley, 1979. | MR 554920 | Zbl 0422.60001

[35] Wolfgang König and Neil O'Connell. Eigenvalues of the Laguerre process as non-colliding squared Bessel processes. Elect. Commun. Probab., to appear. | MR 1871699 | Zbl 1011.15012

[36] Wolfgang König, Neil O'Connell and Sebastien Roch. Non-colliding random walks, tandem queues and the discrete ensembles. Elect. J. Probab., to appear. | MR 1887625 | Zbl 1007.60075

[37] H. Matsumoto and M. Yor. A version of Pitman's 2M - X theorem for geometric Brownian motions. C.R. Acad. Sci. Paris 328 (1999), Série I, 1067-1074. | MR 1696208 | Zbl 0936.60076

[38] H. Matsumoto and M. Yor. A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration. Osaka Math J. 38 (2001) 1-16. | MR 1833628 | Zbl 0981.60078

[39] M.L. Mehta. Random Matrices: Second Edition. Academic Press, 1991. | MR 1083764 | Zbl 0780.60014

[40] P.M. Morse. Stochastic properties of waiting lines. Operations Research 3 (1955) 256. | MR 70889

[41] E.G. Muth (1979). The reversibility property of production lines. Management Sci. 25, 152-158. | MR 537320 | Zbl 0419.90044

[42] I. Norros and P. Salminen. On unbounded Brownian storage. Preprint.

[43] G.G. O'Brien. Some queueing problems. J. Soc. Indust. Appl. Math. 2 (1954) 134. | Zbl 0058.34703

[44] Neil O'Connell. Directed percolation and tandem queues. DIAS Technical Report DIAS-APG-9912.

[45] Neil O'Connell and A. Unwin. Collision times and exit times from cones: a duality. Stochastic Process. Appl. 43 (1992), no. 2, 291-301. | MR 1191152 | Zbl 0765.60083

[46] Neil O'Connell and Marc Yor. Brownian analogues of Burke's theorem. Stoch. Proc. Appl. 96 (2) (2001) pp. 285-304. | MR 1865759 | Zbl 1058.60078

[47] Neil O'Connell and Marc Yor. A representation for non-colliding random walks. Elect. Commun. Probab., to appear. | MR 1887169 | Zbl 1037.15019

[48] J.W. Pitman. One-dimensional Brownian motion and the three-dimensional Bessel process. Adv. Appl. Probab. 7 (1975) 511-526. | MR 375485 | Zbl 0332.60055

[49] J.W. Pitman and L.C.G. Rogers. Markov functions. Ann. Probab. 9 (1981) 573-582. | MR 624684 | Zbl 0466.60070

[50] E. Reich. Waiting times when queues are in tandem. Ann. Math. Statist. 28 (1957) 768-773. | MR 93060 | Zbl 0085.34705

[51] Ph. Robert. Réseaux et files d'attente: méthodes probabilistes. Math. et Applications, vol. 35. Springer, 2000. | MR 2117955 | Zbl 0971.60088

[52] T. Seppäläinen. Hydrodynamic scaling, convex duality, and asymptotic shapes of growth models. Markov Proc. Rel. Fields 4, 1-26, 1998. | MR 1625007 | Zbl 0906.60082

[53] W. Szczotka and F.P. Kelly (1990). Asymptotic stationarity of queues in series and the heavy traffic approximation. Ann. Prob. 18, 1232-1248. | MR 1062067 | Zbl 0726.60092

[54] C.A. Tracy and H. Widom. Fredholm determinants, differential equations and matrix models. Comm. Math. Phys. 163 (1994), no. 1, 33-72. | MR 1277933 | Zbl 0813.35110

[55] David Williams. Path decomposition and continuity of local time for one-dimensional diffusions I. Proc. London Math. Soc. 28 (1974), no. 3, 738-768. | MR 350881 | Zbl 0326.60093