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Random matrices, integrable systems and vertex operators.Mathematical Physics & Probability
|Speaker: ||Professor Pierre van Moerbeke, Mathematical Science Reseach Institute|
|Location: ||693 Kerr|
|Start time: ||Tue, Mar 23 1999, 4:10PM|
The purpose of this seminar is to show that, upon introducing
appropriate time-parameters t, matrix models for general beta can be
generated by certain vertex operators. It shows that these matrix models
satisfy Virasoro constraints.
For beta=2, the matrix models are well-known to satisfy the
Toda Lattice, besides the Virasoro constraints. For beta=1,4, they satisfy
the Pfaff lattice. As a general recipe, combining the Lattice equations
with the Virasoro constraints and setting t=0, leads to partial
differential equations for the probabilities of finding the eigenvalues in
an interval for the corresponding random matrix model.