Fluctuations, large deviations and rigidity in hyperuniform systems: a   brief survey
  We present a brief survey of fluctuations and large deviations of particle systems with subextensive growth of the variance. These are called hyperuniform (or superhomogeneous) systems. We then discuss the relation between hyperuniformity and rigidity. In particular we give sufficient conditions for rigidity of such systems in d=1,2. 
Subhro Ghosh, Joel L. Lebowitz
math.PR cond-mat.stat-mech math-ph math.MP