REMARKS ON ABSOLUTE CONTINUITY IN THE CONTEXT OF FREE PROBABILITY AND RANDOM MATRICES

被引：3
|
作者：
Chakrabarty, Arijit [1 ]
Hazra, Rajat Subhra [2 ]
机构：
[1] Indian Stat Inst, Theoret Stat & Math Unit, New Delhi 110016, India
[2] Indian Stat Inst, Theoret Stat & Math Unit, Kolkata, India
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 03期
关键词：
Free multiplicative convolution; absolute continuity; random matrix; FREE CONVOLUTION;
D O I：
10.1090/proc/12752
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：1335 / 1341
页数：7
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