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+   In our paper we study the extension to complex variables of the
+paradigmatic
+model of "complex landscape". We believe it is the first paper to study
+such complex
+"rugged landscapes", a subject of very high interest whose applications
+range from deep networks
+to optimization. In particular, we introduce and study a matrix model that
+has not, to the best of our knowledge
+studied previously, and which plays for the fluctuations around complex
+saddles
+in disordered systems the role played by the well-known semicircle law in
+the real ones.
+Our work is in line with the beautiful
+E *Bogomolny*, O Bohigas, P *Leboeuf* - Physical Review Letters,  1992
+which concerns the roots  one random polynomial of high degree, while ours
+many of low degree.
+We are very sure that sooner or later many new applications of this problem
+will appear, as always
+has been the case of extending into the complex plane the vision of a  real
+problem.
+