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Probability Theory and Related Fields

, Volume 119, Issue 2, pp 256–274 | Cite as

GUEs and queues

  • Yu. Baryshnikov

Abstract.

Consider the process D k , k = 1,2,…, given by
$$$$

B i being independent standard Brownian motions. This process describes the limiting behavior “near the edge” in queues in series, totally asymmetric exclusion processes or oriented percolation. The problem of finding the distribution of D. was posed in [GW]. The main result of this paper is that the process D. has the law of the process of the largest eigenvalues of the main minors of an infinite random matrix drawn from Gaussian Unitary Ensemble.

Keywords

Brownian Motion Random Matrix Large Eigenvalue Exclusion Process Standard Brownian Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Yu. Baryshnikov
    • 1
  1. 1.LAMA, UVSQ, Bâtiment Fermat, 45, avenue États-Unis, 78035 Versailles, France. e-mail: yuliyb@math.uvsq.frFR

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