Basak, Aniran ; Bose, Arup (2010) Balanced random and Toeplitz matrices Electronic Communications in Probability, 15 . pp. 134-148. ISSN 1083-589X
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Official URL: http://ecp.ejpecp.org/article/view/1537
Related URL: http://dx.doi.org/10.1214/ECP.v15-1537
Abstract
Except for the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist share a common property-the number of times each random variable appears in the matrix is (more or less) the same across the variables. Thus it seems natural to ask what happens to the spectrum of the Toeplitz and Hankel matrices when each entry is scaled by the square root of the number of times that entry appears in the matrix instead of the uniform scaling by n-1/2. We show that the LSD of these balanced matrices exist and derive integral formulae for the moments of the limit distribution. Curiously, it is not clear if these moments define a unique distribution.
Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Mathematical Statistics. |
ID Code: | 93937 |
Deposited On: | 30 Jun 2012 08:11 |
Last Modified: | 19 May 2016 06:52 |
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