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Limiting spectral distribution of XX' matrices

Arup Bose;  Sreela Gangopadhyay;  Arnab Sen — 2010

Annales de l'I.H.P. Probabilités et statistiques

The methods to establish the limiting spectral distribution (LSD) of large dimensional random matrices includes the well-known moment method which invokes the trace formula. Its success has been demonstrated in several types of matrices such as the Wigner matrix and the sample covariance matrix. In a recent article Bryc, Dembo and Jiang [ (2006) 1–38] establish the LSD for random Toeplitz and Hankel matrices using the moment method. They perform the necessary counting of terms in...

Product of exponentials and spectral radius of random k-circulants

Arup Bose;  Rajat Subhra Hazra;  Koushik Saha — 2012

Annales de l'I.H.P. Probabilités et statistiques

We consider × random -circulant matrices with → ∞ and = () whose input sequence { }≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + ) moment. We study the asymptotic distribution of the spectral radius, when = + 1. For this, we first derive the tail behaviour of the fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we show that with...

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