We show that Hurwitz numbers may be generated by certain correlation functions which appear in quantum chaos.First, in short we present two different topics: Hurwitz numbers which appear in counting of branched covers of Riemann and Klein surfaces, and the study of spectral correlation functions of products of random matrices which belong to independent (complex) Ginibre ensembles.There are a lot of studies on extracting information about Hurwitz numbers, on the one hand side, from integrable systems, as it was done in [51], [52], [21] and further developed in [43], [44], [6], [7], [23], [48], [27], [66], [15], [18], [49] (see also reviews [29] and [33]) and from matrix integrals [39], [22], [34] on the other hand. (Actually the point that there is a special family of tau functions which were introduced in [35] and in [55] and studied in [56], [25], [53], [24], [59], [58], [26] where links with matrix models were written down which describes perturbation series in coupling constants of a number of matrix models, and these very tau functions, called hypergeometric ones, count also special types of Hurwitz numbers. This article is based on [48], [59] and [54] and it was the content of my talk in Bialowzie meeting "XXXVI Workshop in Geometric Method in Physics, 3-8 June 2017". In the last paper we put known results in quantum chaos [1], [2], [3], The results of our the work should be compared to ones obtained in [31], [5] and [12].
