Long-range algebraic correlations in random matrices induce a transition at H=3/4 in eigenvalue statistics from generalized t-distributions with fat tails to the semicircle law, identified via scaling analysis and simulations.
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Exact analytic moments and ergodicity properties are derived for occupation times in Gaussian and fractional Brownian motions, with universal features identified via infinite ergodic theory and confirmed by simulations.
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Long-Range Correlated Random Matrices
Long-range algebraic correlations in random matrices induce a transition at H=3/4 in eigenvalue statistics from generalized t-distributions with fat tails to the semicircle law, identified via scaling analysis and simulations.
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Ergodic properties of functionals of Gaussian processes
Exact analytic moments and ergodicity properties are derived for occupation times in Gaussian and fractional Brownian motions, with universal features identified via infinite ergodic theory and confirmed by simulations.