Random matrices, non-colliding processes and queues

Neil O'Connell

Séminaire de probabilités de Strasbourg (2002)

  • Volume: 36, page 165-182

How to cite

top

O'Connell, Neil. "Random matrices, non-colliding processes and queues." Séminaire de probabilités de Strasbourg 36 (2002): 165-182. <http://eudml.org/doc/114084>.

@article{OConnell2002,
author = {O'Connell, Neil},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {random matrix; non-colliding process; queueing theory; Brownian motion; eigenvalue; Poisson process; percolation; polymer},
language = {eng},
pages = {165-182},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Random matrices, non-colliding processes and queues},
url = {http://eudml.org/doc/114084},
volume = {36},
year = {2002},
}

TY - JOUR
AU - O'Connell, Neil
TI - Random matrices, non-colliding processes and queues
JO - Séminaire de probabilités de Strasbourg
PY - 2002
PB - Springer - Lecture Notes in Mathematics
VL - 36
SP - 165
EP - 182
LA - eng
KW - random matrix; non-colliding process; queueing theory; Brownian motion; eigenvalue; Poisson process; percolation; polymer
UR - http://eudml.org/doc/114084
ER -

References

top
  1. [1] F. Baccelli, A. Borovkov and J. Mairesse. Asymptotic results on infinite tandem queueing networks. Probab. Theor. Rel. Fields118, n. 3, p. 365-405, 2000. Zbl0976.60088MR1800538
  2. [2] F. Baccelli, G. Cohen, G.J. Olsder and J.-P. Quadrat. Synchronization and Linearity : An Algebra for Discrete Event Systems. Wiley, 1992. Zbl0824.93003MR1204266
  3. [3] J. Baik. Random vicious walks and random matrices. Comm. Pure Appl. Math.53 (2000) 1385-1410. Zbl1026.60071MR1773413
  4. [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. Zbl0932.05001MR1682248
  5. [5] Yu. Baryshnikov. GUES and queues. Probab. Theor. Rel. Fields119 (2001) 256-274. Zbl0980.60042MR1818248
  6. [6] Ph. Biane. Quelques propriétés du mouvement brownien dans un cone. Stoch. Proc. Appl.53 (1994), no. 2, 233-240. Zbl0812.60067MR1302912
  7. [7] Ph. Biane. Théorème de Ney-Spitzer sur le dual de SU(2). Trans. Amer. Math. Soc.345, no. 1 (1994) 179-194. Zbl0814.60064MR1225572
  8. [8] Ph. Bougerol and Th. Jeulin. Paths in Weyl chambers and random matrices. Preprint. MR1942321
  9. [9] P. Brémaud. Point Processes and Queues: Martingale Dynamics. Springer-Verlag, Berlin, 1981. Zbl0478.60004MR636252
  10. [10] P. Brémaud. Markov Chains, Gibbs Fields, Monte-Carlo Simulation, and Queues. Texts in App. Maths., vol. 31. Springer, 1999. Zbl0949.60009MR1689633
  11. [11] P.J. Burke. The output of a queueing system. Operations Research4 (1956), no. 6, 699-704. MR83416
  12. [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. Zbl0979.60038MR1833691
  13. [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. Zbl0965.60074MR1671824
  14. [14] E. Cépa and D. Lépingle. Diffusing particles with electrostatic repulsion. Probab. Th. Rel. Fields107 (1997), no. 4, 429-449. Zbl0883.60089MR1440140
  15. [15] J.W. Cohen. On the queueing process of lanes. Internal reportPhilips Telecommunicatie Industrie, Hilversum (NL). October 2, 1956. 
  16. [16] B. Derrida. Directed polymers in a random medium. Physica A 163 (1990) 71-84. MR1043640
  17. [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. Zbl1033.60085MR1855425
  18. [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. Zbl1030.91029MR1960566
  19. [19] D. Dufresne. An affine property of the reciprocal Asian option process. Osaka Math J.38 (2001) 17-20. Zbl0987.60026MR1833627
  20. [20] D. Dufresne. The integral of geometric Brownian motionAdv. Appl. Probab.33(1), (2001) 223-241. Zbl0980.60103MR1825324
  21. [21] F.J. Dyson. A Brownian-motion model for the eigenvalues of a random matrix. J. Math. Phys.3 (1962) 1191-1198. Zbl0111.32703MR148397
  22. [22] P.J. Forrester. Random walks and random permutations. Preprint, 1999. (XXX: math.CO/9907037) Zbl0982.82016MR1752728
  23. [23] A.J. Ganesh. Large deviations of the sojourn time for queues in series. Ann. Oper. Res.79:3-26, 1998. Zbl0896.90095MR1630872
  24. [24] P.W. Glynn and W. Whitt. Departures from many queues in series. Ann. Appl. Prob.1 (1991), no. 4, 546-572. Zbl0749.60090MR1129774
  25. [25] D. Grabiner. Brownian motion in a Weyl chamber, non-colliding particles, and random matrices. Ann. IHP35 (1999), no. 2, 177-204. Zbl0937.60075MR1678525
  26. [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. Zbl0989.82030MR1830441
  27. [27] B.M. Hambly, James Martin and Neil O'Connell. Concentration results for a Brownian directed percolation problem. Preprint. Zbl1075.60562MR1935124
  28. [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. Zbl0985.60070MR1855343
  29. [29] J.M. Harrison and R.J. Williams. On the quasireversibility of a multiclass Brownian service station. Ann. Probab.18 (1990) 1249-1268. Zbl0709.60081MR1062068
  30. [30] D. Hobson and W. Werner. Non-colliding Brownian motion on the circle, Bull. Math. Soc.28 (1996) 643-650. Zbl0853.60060MR1405497
  31. [31] K. Johansson. Shape fluctuations and random matrices. Commun. Math. Phys.209 (2000) 437-476. Zbl0969.15008MR1737991
  32. [32] K. Johansson. Discrete orthogonal polynomial ensembles and the Plancherel measure, Ann. Math. (2) 153 (2001), no. 1, 259-296. Zbl0984.15020MR1826414
  33. [33] I.M. Johnstone. On the distribution of the largest principal component. Ann. Stat.29, No. 2 (2001). Zbl1016.62078MR1863961
  34. [34] F.P. Kelly. Reversibility and Stochastic Networks. Wiley, 1979. Zbl0422.60001MR554920
  35. [35] Wolfgang König and Neil O'Connell. Eigenvalues of the Laguerre process as non-colliding squared Bessel processes. Elect. Commun. Probab., to appear. Zbl1011.15012MR1871699
  36. [36] Wolfgang König, Neil O'Connell and Sebastien Roch. Non-colliding random walks, tandem queues and the discrete ensembles. Elect. J. Probab., to appear. Zbl1007.60075MR1887625
  37. [37] H. Matsumoto and M. Yor. A version of Pitman's 2M — X theorem for geometric Brownian motions. C.R. Acad. Sci.Paris328 (1999), Série I, 1067-1074. Zbl0936.60076MR1696208
  38. [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. Zbl0981.60078MR1833628
  39. [39] M.L. Mehta. Random Matrices: Second Edition. Academic Press, 1991. Zbl0780.60014MR1083764
  40. [40] P.M. Morse. Stochastic properties of waiting lines. Operations Research3 (1955) 256. MR70889
  41. [41] E.G. Muth (1979). The reversibility property of production lines. Management Sci.25, 152-158. Zbl0419.90044MR537320
  42. [42] I. Norros and P. Salminen. On unbounded Brownian storage. Preprint. 
  43. [43] G.G. O'Brien. Some queueing problems. J. Soc. Indust. Appl. Math.2 (1954) 134. Zbl0058.34703
  44. [44] Neil O'Connell. Directed percolation and tandem queues. DIAS Technical Report DIAS-APG-9912. 
  45. [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. Zbl0765.60083MR1191152
  46. [46] Neil O'Connell and Marc Yor. Brownian analogues of Burke's theorem. Stoch. Proc. Appl.96 (2) (2001) pp. 285-304. Zbl1058.60078MR1865759
  47. [47] Neil O'Connell and Marc Yor. A representation for non-colliding random walks. Elect. Commun. Probab., to appear. Zbl1037.15019MR1887169
  48. [48] J.W. Pitman. One-dimensional Brownian motion and the three-dimensional Bessel process. Adv. Appl. Probab.7 (1975) 511-526. Zbl0332.60055MR375485
  49. [49] J.W. Pitman and L.C.G. Rogers. Markov functions. Ann. Probab.9 (1981) 573-582. Zbl0466.60070MR624684
  50. [50] E. Reich. Waiting times when queues are in tandem. Ann. Math. Statist.28 (1957) 768-773. Zbl0085.34705MR93060
  51. [51] Ph. Robert. Réseaux et files d'attente: méthodes probabilistes. Math. et Applications, vol. 35. Springer, 2000. Zbl0971.60088MR2117955
  52. [52] T. Seppäläinen. Hydrodynamic scaling, convex duality, and asymptotic shapes of growth models. Markov Proc. Rel. Fields4, 1-26, 1998. Zbl0906.60082MR1625007
  53. [53] W. Szczotka and F.P. Kelly (1990). Asymptotic stationarity of queues in series and the heavy traffic approximation. Ann. Prob.18, 1232-1248. Zbl0726.60092MR1062067
  54. [54] C.A. Tracy and H. Widom. Fredholm determinants, differential equations and matrix models. Comm. Math. Phys.163 (1994), no. 1, 33-72. Zbl0813.35110MR1277933
  55. [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. Zbl0326.60093MR350881

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.