GUEs and queues

Yu Baryshnikov

Research output: Contribution to journalArticlepeer-review

114 Citations (Scopus)

Abstract

Consider the process Dk, k = 1,2, . . ., given by (equation presented) Bi 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.

Original languageEnglish
Pages (from-to)256-274
Number of pages19
JournalProbability Theory and Related Fields
Volume119
Issue number2
DOIs
Publication statusPublished - Feb 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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