Scaled Limit and Rate of Convergence for the Largest Eigenvalue from the Generalized Cauchy Random Matrix Ensemble

In this paper, we are interested in the asymptotic properties for the largest eigenvalue of the Hermitian random matrix ensemble, called the Generalized Cauchy ensemble GCyE, whose eigenvalues PDF is given by

const·?1 ￡ j < k ￡ N(xj-xk)2?j=1N(1+ixj)-s-N(1-ixj)-`(s)]-Ndxj,\textrm{const}\cdot\prod_{1\leq j
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