Remarks on absolute continuity in the context of free probability and random matrices

Arijit Chakrabarty, Rajat Subhra Hazra
2015 Proceedings of the American Mathematical Society  
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. 2010 Mathematics Subject Classification. Primary 60B20; Secondary 46L54, 46L53.
doi:10.1090/proc/12752 fatcat:uyreys4i75bqpox2iywkej3vyy