[hal-01076757] Limiting spectral distribution of Gram matrices associated with functionals of β-mixing processes

We give asymptotic spectral results for Gram matrices of the form n −1 X n X T n where the entries of X n are dependent across both rows and columns and that are functionals of absolutely regular sequences and have only finite second moments We derive under mild dependence conditions in addition to an arithmetical decay condition on the β-mixing coefficients an integral equation of the Stieltjes transform of the limiting spectral distribution of n −1 X n X T n in terms of the spectral density of the underlying process Applications to examples of positive recurrent Markov chains and dynamical systems are also given



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