1212.4467 (Jinho Baik et al.)

Discrete Toeplitz/Hankel determinants and the width of non-intersecting
processes    [PDF]

Jinho Baik, Zhipeng Liu

We prove a simple identity between discrete Toeplitz or Hankel determinants and a Freholm determinant involving continuous orthogonal polynomials. This identity is then used to study triple scaling asymptotics of Toeplitz or Hankel determinants. As a concrete example, we study the width of non-intersecting processes and show that the asymptotic fluctuations of the width are given by the GUE Tracy-Widom distribution. From a separate consideration, we show an identity between the GUE Tracy-Widom distribution and the maximum of the sum of two independent Airy processes minus a parabola.

View original: http://arxiv.org/abs/1212.4467