2011
DOI: 10.1016/j.spl.2011.08.016
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A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth

Abstract: This paper can be thought of as a remark of [5], where the authors studied the eigenvalue distribution µX N of random block Toeplitz band matrices with given block order m. In this note we will give explicit density functions of lim N→∞ µX N when the bandwidth grows slowly. In fact, these densities are exactly the normalized one-point correlation functions of m × m Gaussian unitary ensemble (GUE for short). The series { lim N→∞ µX N |m ∈ N} can be seen as a transition from the standard normal distribution to s… Show more

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Cited by 1 publication
(2 citation statements)
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“…From the above regression equations established, the color (HD65) in physiochemical indexes of red wine has lesser extent related to the physiochemical indexes of wine grapes and only has 38.72% of the goodness of fit to anthocyanins, tannins, sugar and fruit color a *. Color (CD65) also shows the general goodness of fit and only has 58.87% of the goodness of fit to anthocyanins, skin color a * and skin color C. For the five other Physicochemical indexes of red wine, most showed strong correlation to the physiochemical indexes of the wine grape (Li et al, 2011).…”
Section: Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…From the above regression equations established, the color (HD65) in physiochemical indexes of red wine has lesser extent related to the physiochemical indexes of wine grapes and only has 38.72% of the goodness of fit to anthocyanins, tannins, sugar and fruit color a *. Color (CD65) also shows the general goodness of fit and only has 58.87% of the goodness of fit to anthocyanins, skin color a * and skin color C. For the five other Physicochemical indexes of red wine, most showed strong correlation to the physiochemical indexes of the wine grape (Li et al, 2011).…”
Section: Resultsmentioning
confidence: 99%
“…Each wine-tasting gives a score to classification index of wine after the tasting of the wines, then summed to obtain the total score to determine the quality of the wine. There is a direct relationship between the quality of Wine grapes and the quality of Wines, so the physiochemical indexes of Wine and Wine grapes will reflect the quality of the Wines and Wine grapes to some extent (Li et al, 2011). The examples give the composition data of some Wines and Wine grapes in a given year.…”
Section: Introductionmentioning
confidence: 99%