Painlevé I asymptotics for orthogonal polynomials with respect to a varying quartic weight

@inproceedings{Duits2008PainlevIA,
  title={Painlev{\'e} I asymptotics for orthogonal polynomials with respect to a varying quartic weight},
  author={Maurice Duits and Arno B. J. Kuijlaars},
  year={2008}
}
We study polynomials that are orthogonal with respect to a varying quartic weight exp(−N(x2/2+tx4/4)) for t < 0, where the orthogonality takes place on certain contours in the complex plane. Inspired by developments in 2D quantum gravity, Fokas, Its, and Kitaev, showed that there exists a critical value for t around which the asymptotics of the recurrence coefficients are described in terms of exactly specified solutions of the Painlevé I equation. In this paper, we present an alternative and… CONTINUE READING