Limiting spectral distribution of the product of truncated Haar unitary\n matrices

2018/07/19 by Kartick Adhikari, Adhikari, Kartick, Arup Bose +1
Mathematics · #46L54 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1807.07240

openalex publication_date 2018/07/19 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

Let A_m⁽¹⁾,\…, A_m^(k) be m\× m left-uppermost blocks of k\nindependent n\× n Haar unitary matrices where \(n)/(m)\→ \α as\nm\→ \∞, with 1<\α<\∞. Using free probability and Brown measure\ntechniques, we find the limiting spectral distribution of A_m⁽¹⁾\⋯\nA_m^(k).\n

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