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The classical <i>β</i>-ensembles with <i>β</i> proportional to 1/<i>N</i>: From loop equations to Dyson’s disordered chain
In the classical β-ensembles of random matrix theory, setting β = 2α/N and taking the N → ∞ limit gives a statistical state depending on α. Using the loop equations for the classical β-ensembles, we study the corresponding eigenvalue density, its moments, covariances of monomial linear statistics, and the moments …