The N-scaled fluctuations of empirical eigenvalue measures of generalized Wishart processes and related particle systems converge to explicit Gaussian processes, yielding CLTs for Wishart, Dyson Brownian motion, and Ornstein-Uhlenbeck matrix eigenvalues.
High-dimensional limits of eigenvalue distributions for general Wishart process
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abstract
In this article, we obtain an equation for the high-dimensional limit measure of eigenvalues of generalized Wishart processes, and the results is extended to random particle systems that generalize SDEs of eigenvalues. We also introduce a new set of conditions on the coefficient matrices for the existence and uniqueness of a strong solution for the SDEs of eigenvalues. The equation of the limit measure is further discussed assuming self-similarity on the eigenvalues.
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High-dimensional central limit theorems for eigenvalue distributions of generalized Wishart processes
The N-scaled fluctuations of empirical eigenvalue measures of generalized Wishart processes and related particle systems converge to explicit Gaussian processes, yielding CLTs for Wishart, Dyson Brownian motion, and Ornstein-Uhlenbeck matrix eigenvalues.