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


Authors: Arijit Chakrabarty and Rajat Subhra Hazra
Journal: Proc. Amer. Math. Soc. 144 (2016), 1335-1341
MSC (2010): Primary 60B20; Secondary 46L54, 46L53
DOI: https://doi.org/10.1090/proc/12752
Published electronically: June 30, 2015
MathSciNet review: 3447683
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Abstract: 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.


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Additional Information

Arijit Chakrabarty
Affiliation: Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, New Delhi, India
Email: arijit@isid.ac.in

Rajat Subhra Hazra
Affiliation: Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, India
Email: rajatmaths@gmail.com

DOI: https://doi.org/10.1090/proc/12752
Keywords: Free multiplicative convolution, absolute continuity, random matrix
Received by editor(s): September 6, 2014
Received by editor(s) in revised form: February 5, 2015
Published electronically: June 30, 2015
Additional Notes: The research of both authors was supported by their respective INSPIRE grants from the Department of Science and Technology, Government of India
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2015 American Mathematical Society

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