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Kouachi [6], we generalized the above results concerning the eigenvalues of tridiagonal matrices (1) satisfying condition (2), but we were unable to calculate the
Abstract : The Green function of a transient symmetric Markov process can be interpreted as the covariance of a centered Gaussian process.. This relation leads to several
It turns out that if the ratio of the band width to the matrix size decreases to zero as the matrices grow, then it is possible to adjust the matrices in such a way that the
Although the exact convergence rate remains unknown for Wigner matrices, Bai and Yao [ 6 ] proved that the spectral empirical process of Wigner matrices indexed by a set of
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
Various results for the global regime were established (Wigner semicircle law (22), large deviations for the spectral measure (5)...); the statistics of the spacings between
Key words: random fields, Gaussian processes, fractional Brownian motion, fractal mea- sures, self–similar measures, small deviations, Kolmogorov numbers, metric entropy,
We provide a characterisation of Gaussian time series which optimise the one-step prediction error subject to the covariance sequence being completely monotone with the first m
