# Mathematics Colloquia and Seminars

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### From random words to random matrices by quantum statistics

**Mathematical Physics & Probability**

Speaker: | Greg Kuperberg, Mathematics, UC Davis |

Location: | 693 Kerr |

Start time: | Tue, Nov 9 1999, 4:10PM |

Random matrix theorists have recently established that the shape, in the sense of the Robinson-Schensted-Knuth algorithm, of a random word over a k-letter alphabet converges in distribution to the spectrum of a random k by k matrix. In particular, the length of the longest weakly increasing subsequence behaves as the largest eigenvalue.

In this talk, I will construct the matrix itself as a random variable over the probability space of words. The matrix is a quantum random variable rather than a classical one. The construction generalizes to an arbitrary finite-dimensional representation of an arbitrary compact simple Lie algebra, where the original question is associated with the defining representation of su(k).