The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincaré-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical distribution functions associated with high-dimensional random matrices.
The paper REF examines the concentration of empirical distributions for non-independent sequences satisfying Poincaré or log-Sobolev inequalities.
Concentration of empirical distribution functions with applications to non-i.i.d. models
Bernoulli 2010, Vol. 16, No. 4, 1385-1414
Mathematics