A deletion-invariance property for random measures satisfying the   Ghirlanda-Guerra identities
  We show that if a discrete random measure on the unit ball of a separable Hilbert space satisfies the Ghirlanda-Guerra identities then by randomly deleting half of the points and renormalizing the weights of the remaining points we obtain the same random measure in distribution up to rotations. 
Dmitry Panchenko
math.PR