Mathematics Colloquia and Seminars

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Description

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).