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Remarks on absolute continuity in the context of free probability and random matrices. (English) Zbl 1332.60027

Summary: 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.

MSC:

60B20 Random matrices (probabilistic aspects)
46L54 Free probability and free operator algebras
46L53 Noncommutative probability and statistics
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