Remarks on absolute continuity in the context of free probability and   random matrices
  In this note, we show that the limiting spectral distribution of symmetric random matrices with stationary entries is absolutely continuous under some sufficient conditions. This result is applied to obtain sufficient conditions on a probability measure for its free multiplicative convolution with the semicircle law to be absolutely continuous. 
Arijit Chakrabarty and Rajat Subhra Hazra
math.PR