Limiting spectral distribution of circulant type matrices with dependent inputs

作者：Bose Arup^*; Hazra Rajat Subhra; Saha Koushik

来源：Electronic Journal of Probability, 2009, 14(0): 2463-2491.

DOI：10.1214/ejp.v14-714

• Large dimensional random matrix
• eigenvalues
• circulant matrix
• symmetric circulant matrix
• reverse circulant matrix
• k circulant matrix
• empirical spectral distribution
• limiting spectral distribution
• moving average process
• spectral density
• normal approximation

Limiting spectral distribution (LSD) of scaled eigenvalues of circulant, symmetric circulant and a class of k-circulant matrices are known when the input sequence is independent and identically distributed with finite moments of suitable order. We derive the LSD of these matrices when the input sequence is a stationary, two sided moving average process of infinite order. The limits are suitable mixtures of normal, symmetric square root of the chisquare, and other mixture distributions, with the spectral density of the process involved in the mixtures.

• 出版日期2009-11-9