The mathematical theory of random polynomials and random matrices has already found many applications in physics. Indeed the Hamiltonian of a complex or chaotic system can often be viewed as such a matrix.

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We were interested in the case of interacting atoms in which the roots of the polynomials -- that is the location of the quantized vortices -- form a regular array. To our surprise we noticed that even for strictly non-interacting atoms, a local order of the vortex distribution remained.

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