Convergence of the spectral radius of a random matrix through its characteristic polynomial

  title={Convergence of the spectral radius of a random matrix through its characteristic polynomial},
  author={Charles Bordenave and Djalil CHAFA{\"I} and David Garc'ia-Zelada},
  journal={Probability Theory and Related Fields},
Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in probability. This result can also be seen as the convergence of the support in the circular law theorem under optimal moment conditions. In the proof we establish the convergence in law of the reciprocal characteristic polynomial to a random analytic function… 

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