Generating series for GUE correlators

  title={Generating series for GUE correlators},
  author={Boris Dubrovin and Di Yang},
  journal={Letters in Mathematical Physics},
We extend to the Toda lattice hierarchy the approach of Bertola et al. (Phys D Nonlinear Phenom 327:30–57, 2016; IMRN, 2016) to computation of logarithmic derivatives of tau-functions in terms of the so-called matrix resolvents of the corresponding difference Lax operator. As a particular application we obtain explicit generating series for connected GUE correlators. On this basis an efficient recursive procedure for computing the correlators in full genera is developed. 

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