The analytic structure of Rational Interpolants (R.I.) f (z) built from randomly perturbed data is explored; the interpolation nodes x_j, j=1,…, M, are real points where the function f reaches these prescribed data ψ~(m)_(n) (m is the degree of the numerator/denominator). Much attention is paid to the R.I. family f~(m+1)_(n+1), in the small stochasticity regime. The main result is that the additional zero and Pole are located nearby the root of the same random polynomial, called the Froissart Polynomial (F.P.).
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