Random words and isomonodromy deformations
Alexander Its
Abstract:
We show that the integrable system underlying the
finite $N$ inhomogeneous random word model coincides with
the Schlesinger system of isomonodromy deformations of the
$2 \times 2$ matrix linear ODE which has a finite number of simple
poles in the finite complex plane and one Poincar\'e index 1
irregular singular point at infinity.
(Joint work with G. Tracy and H. Widom.)