We apply the method of determinants to study the distribution of the largest singular values of large real rectangular random matrices with independent Cauchy entries. We show that for a special one-parametric class of statistics the properties of the largest singular values (rescaled by a factor ) agree in the limit with the statistical properties of the Poisson random point process with the intensity and, therefore, are different from the Tracy–Widom law. Among other corollaries of our method we show an interesting connection between the mathematical expectations of the determinants of the complex rectangular standard Wishart ensemble and the real rectangular standard Wishart ensemble.
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