Spectral norm of circulant type matrices with heavy tailed entries

Arup Bose (Indian Statistical Institute, Kolkata)
Rajat Subhra Hazra (Indian Statistical Institute, Kolkata)
Koushik Saha (Indian Statistical Institute, Kolkata)

Abstract


We first study the probabilistic properties of the spectral norm of scaled eigenvalues of large dimensional Toeplitz, circulant and symmetric circulant matrices when the input sequence is independent and identically distributed with appropriate heavy tails. When the input sequence is a stationary two sided moving average process of infinite order, we scale the eigenvalues by the spectral density at appropriate ordinates and study the limit for their maximums.

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Pages: 299-313

Publication Date: July 23, 2010

DOI: 10.1214/ECP.v15-1554

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