# Mathematics Colloquia and Seminars

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### Random walks, queues, Young tableaux and random matrices

**Colloquium**

Speaker: | Neil O'Connell, Ecole Normale Superiour |

Location: | 693 Kerr |

Start time: | Mon, Apr 15 2002, 4:10PM |

In an attempt to understand recently observed connections between longest increasing subsequence problems and random matrices, and to give a multi-dimensional version of Pitman's representation for a Brownian motion conditioned to stay positive, we obtain a representation for independent random walks (or Brownian motions) conditioned never to collide. The proof uses a classical theorem of queueing theory on the output of a single-server queue, and certain symmetries associated with many queues in series. I will also describe how this is connected with the RSK correspondence, and what we can learn from this connection.

(Coffee & cookies @ 3:45 in 550 Kerr )