CONVERGENCE OF JOINT MOMENTS FOR INDEPENDENT RANDOM PATTERNED MATRICES

• 成果类型: Article
• 署名作者: Bose, Arup; Hazra, Rajat Subhra; Saha, Koushik
• 署名单位: Indian Statistical Institute; Indian Statistical Institute Kolkata
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP597
• 发表日期: 2011
• 页码: 1607-1620
• 关键词: dimensional random matrices

摘要

It is known that the joint limit distribution of independent Wigner matrices satisfies a very special asymptotic independence, called freeness. We study the joint convergence of a few other patterned matrices, providing a framework to accommodate other joint laws. In particular, the matricial limits of symmetric circulants and reverse circulants satisfy, respectively, the classical independence and the half independence. The matricial limits of Toeplitz and Hankel matrices do not seem to submit to any easy or explicit independence/dependence notions. Their limits are not independent, free or half independent.