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.
"Concentration of empirical distribution functions with applications to non-i.i.d. models." Bernoulli 16 (4) 1385 - 1414, November 2010. https://doi.org/10.3150/10-BEJ254