Generating series for GUE correlators |
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Authors: | Boris Dubrovin Di Yang |
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Institution: | 1.SISSA,Trieste,Italy;2.N. N. Bogolyubov Laboratory of Geometrical Methods in Mathematical Physics, Department of Mechanics and Mathematics,Moscow State University “M.V.Lomonosov”,Moscow,Russia |
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Abstract: | 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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