  We study the fluctuations associated to the a.s. convergence, established by
Belinschi-Bercovici-Capitaine, of the outliers of an Hermitian polynomial in a
complex Wigner matrix and a spiked deterministic real diagonal matrix. Thus, we
extend the non universality phenomenon previously established for additive
deformations of complex Wigner matrices, to any Hermitian polynomial. The
result is described using the operator-valued subordination functions of free
probability theory.
