On tau-functions for the Toda lattice hierarchy

We extend a recent result of Dubrovin et al. in On tau-functions for the KdV hierarchy, arXiv:1812.08488 to the Toda lattice hierarchy. Namely, for an arbitrary solution to the Toda lattice hierarchy, we define a pair of wave functions and use them to give explicit formulae for the generating series of k-point correlation functions of the solution. Applications to computing GUE correlators and Gromov–Witten invariants of the Riemann sphere are under consideration.