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From random words to random matrices by quantum statisticsMathematical 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).