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On the largest singular values of random matrices with independent Cauchy entries (2005)
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| Venue: | J. MATH. PHYS |
| Citations: | 7 - 0 self |
BibTeX
@ARTICLE{Soshnikov05onthe,
author = {Alexander Soshnikov and Yan V. Fyodorov},
title = {On the largest singular values of random matrices with independent Cauchy entries},
journal = {J. MATH. PHYS},
year = {2005},
volume = {46},
pages = {33302}
}
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Abstract
We apply the method of determinants to study the distribution of the largest singular values of large m × n real rectangular random matrices with independent Cauchy entries. We show that statistical properties of the (rescaled by a factor 1 m 2 n 2) largest singular values agree in the limit with the statistics of the Poisson random point process with the intensity 1 π x−3/2 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 m×n standard Wishart ensemble and the real rectangular 2m×2n standard Wishart ensemble.
