  We investigate overlap fluctuations of the Sherrington-Kirkpatrick mean field
spin glass model in the framework of the Random Over- lap Structure (ROSt). The
concept of ROSt has been introduced recently by Aizenman and coworkers, who
developed a variational approach to the Sherrington-Kirkpatrick model. We
propose here an iterative procedure to show that, in the so-called Boltzmann
ROSt, Aizenman-Contucci (AC) polynomials naturally arise for almost all values
of the inverse temperature (not in average over some interval only). The same
results can be obtained in any ROSt, including therefore the Parisi structure.
The AC polynomials impose restric- tions on the overlap fluctuations in
agreement with Parisi theory.
