科研之友
微信
新浪微博
Facebook
分享链接
摘要
We study two specific symmetric random block Toeplitz (of dimension k x k) matrices, where the blocks (of size n x n) are (i) matrices with i.i.d. entries and (ii) asymmetric Toeplitz matrices. Under suitable assumptions on the entries, their limiting spectral distributions (LSDs) exist (after scaling by root nk) when (a) k is fixed and n -> infinity (b) n is fixed and k -> infinity (c) n and k go to infinity simultaneously. Further, the LSDs obtained in (a) and (b) coincide with those in (c) when n or respectively k tends to infinity. This limit in (c) is the semicircle law in Case (i). In Case (ii), the limit is related to the limit of the random symmetric Toeplitz matrix as obtained by Bryc et al. (2006) and Hammond and Miller (2005).
- 出版日期2012-7
