کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5130161 | 1378662 | 2016 | 22 صفحه PDF | دانلود رایگان |
In this paper, we consider a Wigner matrix A with entries whose cumulative distribution decays as xâα with 2<α<4 for large x. We are interested in the fluctuations of the linear statistics Nâ1TrÏ(A), for some nice test functions Ï. The behavior of such fluctuations has been understood for both heavy-tailed matrices (i.e. α<2) in Benaych-Georges (2014) and light-tailed matrices (i.e. α>4) in Bai and Silverstein (2009). This paper fills in the gap of understanding it for 2<α<4. We find that while linear spectral statistics for heavy-tailed matrices have fluctuations of order Nâ1/2 and those for light-tailed matrices have fluctuations of order Nâ1, the linear spectral statistics for half-heavy-tailed matrices exhibit an intermediate α-dependent order of Nâα/4.
Journal: Stochastic Processes and their Applications - Volume 126, Issue 11, November 2016, Pages 3331-3352