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.)