Toward a Classification of Stochastically Stable Quenched Measures
  In this short note we study the fourth order consequences of the stochastic stability property for mean field spin glass models introduced in previous paper by Aizenman and Contucci. We show that due to a remarkable cancellation mechanism it reduces to the well known second order version as predicted by Parisi's replica-equivalent ansatz. 
Pierluigi Contucci