Random Matrices and Queues in Series

Some very simple questions about queues in series (like: When does the customer umber~5 leaves the queue number~6?) are very difficult to answer, unless one reduces them to seemingly more difficult question about random matrices. In my talk I'll show that the queueing process relates to the law of the largest eigenvalues of the main minors of an infinite random matrix drawn from the Gaussian Unitary Ensemble. I will give details of some steps of the reduction, featuring, among others, the Robinson-Schensted-Knuth correspondence between Young tableaux and permutations.