Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900334 | Journal of Mathematical Analysis and Applications | 2018 | 19 Pages |
Abstract
Consider a truncated circular unitary matrix which is a pn by pn submatrix of an n by n circular unitary matrix by deleting the last nâpn columns and rows. Jiang and Qi [11] proved that the maximum absolute value of the eigenvalues (known as spectral radius) of the truncated matrix, after properly normalized, converges in distribution to the Gumbel distribution if pn/n is bounded away from 0 and 1. In this paper we investigate the limiting distribution of the spectral radius under one of the following four conditions: (1). pnââ and pn/nâ0 as nââ; (2). (nâpn)/nâ0 and (nâpn)/(logâ¡n)3ââ as nââ; (3). nâpnââ and (nâpn)/logâ¡nâ0 as nââ and (4). nâpn=kâ¥1 is a fixed integer. We prove that the spectral radius converges in distribution to the Gumbel distribution under the first three conditions and to a reversed Weibull distribution under the fourth condition.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Wenhao Gui, Yongcheng Qi,