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The study of physical systems using probabilistic reasoning, especially relating small-scale classical mechanics to large-scale thermodynamics.
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Matrix model for "$\beta$-Ginibre" ensembles
A very well known result in random matrix theory is that there exists "nice" (i.e., with independent entries) tridiagonal matrix for the $\beta$-ensembles of random matrix theory
$$\propto\prod_{i<j}| …