Remarks on absolute continuity in the context of free probability and random matrices
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- by Arijit Chakrabarty and Rajat Subhra Hazra PDF
- Proc. Amer. Math. Soc. 144 (2016), 1335-1341 Request permission
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.References
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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
- MR Author ID: 888078
- Email: rajatmaths@gmail.com
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1335-1341
- MSC (2010): Primary 60B20; Secondary 46L54, 46L53
- DOI: https://doi.org/10.1090/proc/12752
- MathSciNet review: 3447683